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Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
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Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
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Page 33
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 34
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 35
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 36
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 37
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 38
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 39
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 40
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 41
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 42
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 43
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 44
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 45
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 46
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 47
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 48
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 49
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 50
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 51
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 52
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 53
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 54
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 55
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 56
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 57
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 58
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 59
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 60
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 61
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 62
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 63
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 64
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 65
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 66
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 67
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 68
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 69
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 70
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 71
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 72
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 73
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 74
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 75
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 76
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 77
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 78
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 79
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 80
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 81
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 82
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 83
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 84
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 85
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 86
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 87
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 88
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 89
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 90
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 91
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 92
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 93
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 94
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 95
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 96
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 97
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 98
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 99
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 100
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 101
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 102
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 103
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 104
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 105
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 106
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 107
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 108
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 109
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 110
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 111
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 112
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 113
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 114
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 115
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 116
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
×
Page 117
Suggested Citation:"Chapter 3 - Schedule Building." National Academies of Sciences, Engineering, and Medicine. 2009. Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling. Washington, DC: The National Academies Press. doi: 10.17226/14257.
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Page 118

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Chapter 3. Schedule Building ͯ.ͭ Building a Simple Schedule (Level ͭ) ͯ.ͮ A Slightly More Intricate Schedule (Level ͮA) ͯ.ͯ Working on a More Intricate Schedule (Level ͮB) ͯ.Ͱ Advanced Schedule Building (Level ͯA) ͯ.ͱ Advanced Topics In Schedule Writing (Level ͯB)

Chapter 3. Schedule Building 3-3 Level ͭ. Building a Simple Schedule span of service The length of time, from the begin- ning of the fi rst trip to the end of the last trip, during which service operates on the street. Can be expressed for a route or for the system as a whole. headway The interval of time between two vehicles running in the same direc- tion on the same route, usually expressed in minutes. See also “frequency.” service pattern The unique sequence of stops associated with each type of trip on a route. If all trips operate from one end to the other on a common path the route has one service pat- tern. Branches, deviations, or short turns introduce additional service patterns. Service patterns are a fundamental component of schedul- ing and provide the framework for tracking running time, generating revenue trips, and identifying dead- head movements for the route. deadhead The time and distance that a bus needs to travel in places where it will not pick up passengers. Deadheading is typically required to get buses to and from their garage, or need to travel from one route or point to another during their sched- uled work day. 3.1 Building a Simple Schedule Even a simple schedule reveals some important concepts that apply in one way or another to all scheduling. In fact, the most complicated schedule is no more than a series of the same steps we will talk about here. Do not be misled by our calling this a “simple” schedule. Sometimes the most dif- fi cult schedules are those with the fewest options (i.e., the “simple” ones!). In reality, schedul- ing only becomes simple by doing it over and over again. For this project we will build a straightforward ͯͬ-minute all-day schedule on a single route that operates just one service pattern. Let’s call this Route ͵ͳ—Broad St.—a new route being developed. We are just interested in the weekday schedule for now. Here is what you need to know: Span of Service – Ͳ:ͬͬ AM to ͳ:ͬͬ PM Headway – ͯͬ minutes throughout Service patterns – All trips operated from time point A to time point D. Reverse direc- tion trips from D to A Garage – This route operates out of Park Garage which is nearer to the time point A end of the route Deadhead times to and from the garage are: ͭͬ minutes to/from “A,” ͮͬ minutes to/ from “D” Mileage and running time – shown in the diagram below The upper numbers are minutes between time points, the lower is the mileage. • • • • • • LEVEL 1 BA C D 8 min 14 min 11 min 1.38 min 2.87 min 2.22 minͭ.ͯʹ miles ͮ.ʹͳ miles ͮ.ͮͮ miles

Level ͭ. Building a Simple ScheduleChapter 3. Schedule Building 3-4 Most of this information will come from a service plan or from discussion with planners. It will always be up to you to verify this information, because ultimately the responsibility for the development of the operating schedule falls to you. So, where to start? Here is the general sequence of events: ͭ. Calculate the round-trip cycle time, including layover. ͮ. Figure out how much layover you have and where to apply it. ͯ. Work out the basic schedule pattern. This is the key to the task and includes consider- ation of: The cycle and layover times Contract layover requirements • • Operational preferences Runcut requirements • • Ͱ. Decide where and when (based on the span of service standard discussed in Chapter ͮ) to start service. ͱ. Populate the schedule. Ͳ. Then, and only then, fi ll in the intermediate times, working downward while constantly checking adjacent running times. ͳ. Block your schedule by following the fi rst trip and its subsequent trips (hooks) all the way to the end of the schedule, then fi lling in the rest of the block numbers in the same manner. This and subsequent steps are addressed in Chapter Ͱ: Schedule Blocking. ʹ. Mark your pull-on and pull-off locations for each block, and apply the out or in time to and from the garage. ͵. Build a table of your blocks, showing pull-out and pull-in times and resulting vehicle hours. The table will add up at the bottom to the total vehicle hours for the schedule. ͭͬ. Build a table of mileage along the same principle, yielding total mileage for the schedule. ͭͭ. Proofread your work before declaring the schedule fi nished and ready for the runcut. ͭͮ. If need be, hand the schedule back to the planning staff so they can see what their con- cept looks like when turned into reality. Let’s tackle steps one through six, which are most integral in building a schedule. Steps seven through ͭͮ are discussed separately in Chapter Ͱ: Schedule Blocking. cycle time Sum of the round-trip running time plus layover time. Also known as “round trip cycle time.” schedule pattern A summary of the schedule in terms of running times between time points and layover time at termi- nals. The schedule pattern can be repeated throughout the day or can change as running times and lay- over times change during the day. layover time Time between the scheduled arrival and departure of a vehicle at a transit terminal. Often used inter- changeably with “recovery time,” although technically layover time is rest time for the operator between trips while recovery time is time built into the schedule to ensure an on-time departure for the next trip. In this manual, layover and recov- ery are calculated together and the total time between trips is referred to as “layover.”

Chapter 3. Schedule Building 3-5 Level ͭ. Building a Simple Schedule Round-trip Cycle Time This is the most important concept you will master in building a proper schedule. The round- trip cycle time is: Round-trip running time + required layover Since the round-trip running time must be already calculated and accurate, it is crucial to this formula. On routes where running times vary by time of day, this cycle must be calculated for diff erent times of the day. This example uses the information we have been given for Route ͵ͳ. Working across the diagram on page ͯ-ͭ from left to right (we will call this eastbound) we fi nd running of ʹ, ͭͰ and ͭͭ minutes, which add up to ͯͯ minutes. The same ͯͯ minutes apply west- bound. This gives us a ͲͲ-minute round-trip. To that, an adequate layover must be added. Layover Requirements Layover requirements will be explored in greater detail in the following sections. For now, we will assume some basic principles. Possibly your union contract specifi es a minimum layover either at one end of the route or for a full round-trip. If the union contract does not address layover, past practice may guide the allocation of layover time. An example of minimum lay- over is ͭͬ% of the running time or six minutes per round-trip, whichever is greater. This route might need more than that, depending on propensity for traffi c congestion, a high number of wheelchair boardings, and other operational details that cannot be accurately predicted in the running time. If so, then you will want to add some minutes to that required by the contract or allocated by past practice. In our example, ͭͬ% of ͲͲ would be seven minutes (always round up to the next minute if the percentage is a minimum)—which, added to the running time, would give us a round-trip cycle of ͳͯ minutes. That is the minimum cycle we can operate. Now the tough part comes in. We have to divide the cycle by the intended headway for the period. In this case, we have a requirement for a ͯͬ-minute headway all day. Multiples of ͯͬ are ͯͬ, Ͳͬ, ͵ͬ, ͭͮͬ, etc. We just missed Ͳͬ and we cannot squeeze the running time back to fi t into that cycle. Reducing layover below the minimum or reducing running time below the calcu- lated requirement is taboo, especially once we have determined that we need every bit of the ͲͲ minutes. So we have to see what other options we have. Since the cycle time cannot be shortened, one option would be to extend the round-trip cycle to ͵ͬ minutes, the next highest ͯͬ-minute multiple, requiring ͯ buses (͵ͬ divided by ͯͬ). That would give us a total of ͮͰ minutes of layover, or ͯͲ%—a wasteful amount, with the bus and its 2 1pull-on location The place on a route where a vehicle begins revenue service. pull-off location The place on a route where a vehicle ends revenue service. pull-out time The time the vehicle spends travel- ing from the garage to the route. Pull-out time is included in vehicle hours, but not in revenue hours. Collectively, pull-in time and pull-out time are also known as pull time and are components of deadhead miles. pull-in time The time the vehicle spends travel- ing from the route to the garage. Pull-in time is included in vehicle hours, but not in revenue hours. Collectively, pull-in time and pull-out time are also known as pull time and are components of deadhead time.

Level ͭ. Building a Simple ScheduleChapter 3. Schedule Building 3-6 operator sitting idle one third of the time. But if we have a system set up on pulses at a transit center or other meet point, this may be our only option. In fact, if we generally allow fi ve min- utes of connection time in each direction at a mid-route transit center, this allowance would bring us back to ͭͰ minutes that would be available for end of line layover, or ͮͬ%—a more reasonable number. Another option is to look at a better service level. If we stay to a clockface headway, a ͮͬ-min- ute headway would be our next choice. Progressions of ͮͬ are ͮͬ, Ͱͬ, Ͳͬ, ʹͬ, ͭͬͬ, etc. An ʹͬ- minute cycle would provide ͭͰ minutes of layover and a better frequency, but it would require one more bus to operate the schedule (ʹͬ divided by ͮͬ). Can we aff ord the extra all day bus? An extra bus translates to about ͭͯ extra bus hours for the day, every day. Would a ͮͬ-minute headway work in any connection strategy we might have? Finally, do we really need a ͮͬ-min- ute headway in order to carry the expected ridership levels? If the answer to any of these ques- tions is “no,” then this is not our option. One fi nal option is to look at a non-clockface headway. In this case, a ͮͱ-minute headway with three buses would give us a ͳͱ-minute cycle, which is just three minutes more than our so- called minimum cycle, which is just fi ne if we can tolerate a ͮͱ-minute headway. The resulting schedule is not easy to remember, but in this case it does have the advantage of providing two extra round-trips during the operating day for the same number of buses and bus hours. While clockface headways are nice, the reality is that most people will consult a timetable for any service that is less frequent than every ͭͱ minutes. One other possibility exists—which is to use the extra time available to extend the route and increase coverage. This kind of route adjustment to fi t the schedule is usually done when ini- tially planning and scheduling the route or when considering a route extension. This is a good example of why there has to be a working collaboration process between planners and sched- ulers. Route design should always seek to take advantage of scheduling effi ciencies and, more importantly, avoid creating ineffi ciencies. Since our schedule is a simple one, with the same headway and running time all day, we only need to calculate one round-trip cycle and make one determination as to where to apply the layover. This strategy will work all day. We will see examples of schedules with lots of variations in the intermediate and advanced sections later in this chapter. Never reduce a mini- mum required layover time or calculated running time to “squeeze” the cycle to better fi t the headway. Tip transit center An area designed to be served by multiple routes. A transit center may be on-street or off-street, but in either case stop locations are established to facilitate passenger connections and safe vehicle move- ment. In radial networks, transit centers were located in downtown areas. With the emergence of hub- and-spoke networks, an agency may utilize multiple transit centers (or hubs). timetable A document containing route and time information produced for use by riders.

Chapter 3. Schedule Building 3-7 Level ͭ. Building a Simple Schedule In this example, we have decided on the ͯͬ-minute headway using three buses. The excess layover time is not desirable, but works to our advantage for a route that connects with other routes in our system at a mid-route timed transfer point. We will discuss timed transfer schemes in a later section. Basic Schedule Pattern Most basic schedules are laid out either using spreadsheets or computerized systems. For this exercise we will assume a spreadsheet is being used. There are some important issues to consider about spreadsheet design. These include: Simplicity. Avoid getting too complex with presentation. Use basic colors. Location of inputs and outputs. Think about who will look at the sheet, and how it will be used. Should fi xed inputs (running times, mileage, etc.) be hidden to the side, on a separate sheet, or readily visible? Use of formulas. We will state repeatedly throughout this manual the importance of accuracy. Spreadsheets are terrifi c tools for minimizing repetitive work. They also pres- ent pitfalls, as errors can be diffi cult to fi nd and/or trace. The key principle in design of a headway sheet should be to use formulas as much as possible—if you can avoid typing a number that can be calculated, do so! Why? There are two main reasons. First, the need to avoid errors, which are more likely to occur through manually typing numbers. Secondly, schedules inevitably change (you will see an example shortly). The more automated a sheet is, the easier (and less prone to error) the change process will be. If you want to highlight things, consider use of conditional formatting. As you will see on the sample spreadsheet, there are only two typed values. The rest are formulas. • • • 3 Time point placement is important. You do not want these points too close together nor too far apart. They should be at major intersections or other major points along the route, as the public will look for exact times at these points on the printed timetable. A rule of thumb is that time points are ideally spaced between about 7 and 15 minutes apart, or an average of about 10 minutes between each one. Beyond the need to inform the public of scheduled arrival times, time points serve to help drivers “pace themselves” when driving the route. The scheduler should also ensure that bus stops exist in both directions at a time point, to avoid confusing the riding public. Tip

Level ͭ. Building a Simple ScheduleChapter 3. Schedule Building 3-8 In laying out the schedule, it is a lot easier to have the two directions placed side by side. You can see the fl ow of the schedule better that way, although it does take some prior planning on how you lay out the sheet. Start preparing the headway sheet or master schedule by naming the columns across the top. Start with the Eastbound direction fi rst (that is our preference, but it can work to start with westbound fi rst if you have a compelling reason to do so…or just favor doing it that way). Column A is for the block number. Here is where we will keep track of the bus rotation in the schedule. Column B is for Pull-Out times or the time the bus leaves the garage. Columns C through F are time points by name, in our case A, B, C, and D. Leave Column G blank and start back westbound with time points D, C, B, and A. Then leave Column L blank and label Column M Next Trip. Column M is where you will keep track of hooking round-trips to their next trips or, when running out of trips, will indicate by a blank that they become a pull-in. Follow that with Column N for Pull-in. Your spreadsheet will look like this: A quick note about the term “block.” This is the term for the vehicle (bus, light rail vehicle or train, heavy rail train, etc.) assignment, which describes what the vehicle will do in a day. Some systems call this a “train” or a “run” or even a “key.” We use “block” because that is the prevail- ing term in the industry and is less likely to be confused with “run,” which is predominantly applied to the driver, not the vehicle, assignment. A B C D E F G H I J K L M N 1 Example Headway Sheet #1 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip Pull In Eastbound Westbound master schedule A document that displays all time points and trips on a route. Usu- ally includes run numbers, block numbers, and pull-in and pull-out times. Used interchangeably in this manual with “headway sheet.” block A vehicle (or train) assignment that includes the series of trips oper- ated by each vehicle from the time it pulls out to the time it pulls in. A complete block includes a pull-out trip from the garage followed by one or (usually) more revenue trips and concluding with a pull-in trip back to the garage. hooking The process of attaching the end of a trip in one direction to the begin- ning of a trip the other direction. A block is a series of hooked trips. round-trip A trip that travels along a route and then returns to its original starting point; a combination of two one-way trips on a route.

Chapter 3. Schedule Building 3-9 Level ͭ. Building a Simple Schedule We start by noting down some basic information—the running time and distance between time points in each direction and the headway, for starters. We will put this out of the way, to the right of the schedule, in columns P through R, as shown here. We also add in time and mileage from the garage to the two end points of the route. Before we start writing in trip times, we take a step backwards—to the answer! One of the key tenets of scheduling is to know the answer before you jump into the detail. In this case, looking at a few simple calcula- tions (as we did above), we can see how everything will pan out before we write any schedules. The key to this is the development of a schedule pat- tern. This concept can be applied to the simplest sched- ules as eff ectively as it can be applied to a ͭͬ-route interline with complex branching patterns. The schedule pattern in eff ect summarizes the sched- ule, for all or part of a day. In this case, since the running time and headway is constant, the schedule pattern will summarize operation for the entire day. P Q R 1 2 3 4 5 6 7 Run Time Distance 8 A - - 9 B 8 1.4 10 C 14 2.9 11 D 11 2.2 12 Total 33 6.5 13 14 15 16 Run Time Distance 17 D - 18 C 11 2.2 19 B 14 2.9 20 A 8 1.4 21 Total 33 6.5 22 23 24 Garage Deadheads 25 Run Time Distance 26 To "A" 10 3.5 27 To "D" 20 6.8 28 29 30 0:06 31 0:10 32 0:12 33 0:15 34 0:20 35 0:30 36 1:00 Westbound Headway Options Running Time/Mileage Definitions Eastbound Note that we enter vari- ous clock face headway options in time format in cells Q30: Q36. These will remain the same no matter how many times we use this spreadsheet, and the time for- mat saves a step in entering formu- las, as we will see below. Running times are subject to change, and so it is simpler to enter them in general format. Tip

Level ͭ. Building a Simple ScheduleChapter 3. Schedule Building 3-10 First, we enter a time for the fi rst eastbound trip. We start with Ͳ:ͬͬ and our schedule pattern sheet looks like this: The arrival time at Point D, the end of the route, is a simple formula that takes the depart time cell and adds the running time (also defi ned in the spreadsheet). The formula can be entered in one of two ways: =Cͳ+(ͬ.ͬͬͬͲ͵ͰͰͰ*Qͭͮ) or =Cͳ+time(ͬ,Qͭͮ,ͬ). We already have half the schedule pattern complete and are well on the way to creating our schedule. Next we look at the return trip. It needs to depart no earlier than Ͳ:ͯͳ (based on the minimum Ͱ-minute layover). We are now faced with making a decision as to where to apply our ͮͰ minutes of layover time. We can apply it evenly—ͭͮ minutes at each end—or we can provide diff erent layover times at each end. In real-world operations, there are concerns with laying over for too long at some locations, which would help make our decision. On some systems, it is standard practice to give no layover at the outer terminal and allow the buses to take their time at the downtown or transit center point on the route. Others without an off -street transit center downtown may give minimal layover downtown and allocate most of its layover time at the outer terminal. In this case, we will apply ͭͮ minutes to each end of the route. That will give us leaving times from “D” at :ͭͱ and :Ͱͱ past the hour. Having made that decision we update our schedule pattern to look like this: A B C D E F G H I J K L M 1 Example Headway Sheet #1 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip 6 7 6:00 6:33 Eastbound Westbound A B C D E F G H I J K L M 1 Example Headway Sheet #1 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip 6 7 6:00 6:33 6:45 7:18 7:30 Eastbound Westbound The factor 0.00069444 converts a regularly formatted number to minutes in the time format. This factor is equiva- lent to 1/24/60. An alternate entry is TIME (x,y,z), where x is hours, y is minutes, and z is seconds. Using this, the equation in the second row under B would be “=C7 + TIME (0, Q12,0).” Tip terminal One end point of a route where trips usually begin and end.

Chapter 3. Schedule Building 3-11 Level ͭ. Building a Simple Schedule Guess what? The schedule is now eff ectively built! First we need to check a couple of things: ͭ. How many buses? If our bus arrives back at “A” at ͳ:ͭʹ, and there are departures at :ͬͬ and :ͯͬ, its next possible trip would be the ͳ:ͯͬ trip. Is that correct according to our plan? Yes—it produces a ͭͮ-minute layover at each end. So how many buses do we need? This becomes a simple calculation of dividing the cycle time (inclusive of scheduled layover) by the headway. In this case, ͵ͬ minutes (i.e., ͳ:ͯͬ minus Ͳ:ͬͬ) divided by the ͯͬ-minute headway is three—and there is our answer, three buses! ͮ. Are we happy with the times at the ends, and any key intermediate points? We now have a schedule pattern that we simply begin at the start of the day and end when we want our service to end. And we know how many buses we need. Decide When to Start Service We still need to decide when the fi rst trip should start in each direction. Our service plan says that service will operate from Ͳ:ͬͬ AM to ͳ:ͬͬ PM. Does that mean that we must begin service in both directions at Ͳ:ͬͬ AM? It may be obvious to you who are mathematically inclined at this point that we cannot have a Ͳ:ͬͬ AM leaving time at the “D” point once we have decided to leave from “A” on the hour and the half-hour. A Ͳ:ͯͯ AM arrival at “A” would not have another trip until ͳ:ͬͬ AM, which would be too late in returning to “D” to make the ͳ:ͯͬ next trip. We would end up with four buses instead of three on this route. So, what now? We are meeting the goals of the service plan by starting promptly at Ͳ:ͬͬ AM eastbound. But our schedule pattern calls for the westbound trip to be either :ͭͱ or :Ͱͱ past the hour. Is Ͳ:ͭͱ early enough to meet the expected demand (or the intent of the service specifi ca- tion), or should we look at a fi rst westbound trip at ͱ:Ͱͱ, one cycle earlier? Knowing your system will help you answer that. The biggest question is whether there is gener- al demand in your community for service at Ͳ:ͬͬ AM or earlier. A lot also depends on expected ridership from the east end of the route as compared to the west end. More people might be expected to travel westbound earlier due to work or school demands. If so, then a ͱ:Ͱͱ AM trip should be the fi rst from that direction. From an effi ciency standpoint, it will be cheaper to start the trips going east, since the garage is closer to that end of the line, but that is generally less important than making sure that the schedule serves the expected ridership. If this were a fi xed 4

Level ͭ. Building a Simple ScheduleChapter 3. Schedule Building 3-12 guideway (light rail or trolley coach) route, then it would be necessary to start out trips earlier than necessary in one direction to assure they are in position to start the service on time in the other direction. In our case, we will make a decision based on the knowledge of our hypotheti- cal system to have the fi rst westbound trip leave point “D” at Ͳ:ͭͱ AM. After adding this trip, your spreadsheet looks like this: One of the beauties of spreadsheets is that if you happened to enter the Ͳ:ͬͬ eastbound trip in Row Ͳ instead of Row ͳ, you could simply insert a row to enter the westbound trip. Populate the Schedule The next step is fi lling out the schedule. Now that we have the basic schedule pattern and have decided on the starting time in both directions, we simply repeat the schedule pattern. So east- bound trips depart “A” at :ͬͬ/:ͯͬ, and westbound trips depart “D” at :ͭͱ/:Ͱͱ. This is easiest to do with a formula, in which we add thirty minutes (the headway, which is located in cell Qͯͱ) to the previous trip. Row ʹ would look like this, using the “show formula” feature: A B C D E F G H I J K L M 1 Example Headway Sheet #1 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip 6 6:15 6:48 7:00 7 6:00 6:33 6:45 7:18 7:30 Eastbound Westbound 5 on time Defi ned specifi cally by each sys- tem, a trip is considered on time if it arrives or departs from a time point within a specifi ed range of time. A typical range is 0 to 5 minutes after the scheduled arrival/departure time. A trip that leaves a time point early is referred to as “hot” or “run- ning hot.”

Chapter 3. Schedule Building 3-13 Level Í­. Building a Simple Schedule Then, after we copy the formula in row Í´ down columns C and H (corresponding to the leave times at points A and D), we have the basic schedule populated throughout the day: A B C D E F G H I J K L M N 1 Example Headway Sheet #1 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip Pull In 6 6:15 6:48 7:00 7 6:00 6:33 6:45 7:18 7:30 8 6:30 7:15 8:00 9 7:00 7:45 8:30 10 7:30 8:15 9:00 11 8:00 8:45 9:30 12 8:30 9:15 10:00 13 9:00 9:45 10:30 14 9:30 10:15 11:00 15 10:00 10:45 11:30 16 10:30 11:15 12:00 17 11:00 11:45 12:30 18 11:30 12:15 13:00 19 12:00 12:45 13:30 20 12:30 13:15 14:00 21 13:00 13:45 14:30 22 13:30 14:15 15:00 23 14:00 14:45 15:30 24 14:30 15:15 16:00 25 15:00 15:45 16:30 26 15:30 16:15 17:00 27 16:00 16:45 17:30 28 16:30 17:15 18:00 29 17:00 17:45 18:30 30 17:30 18:15 19:00 31 18:00 18:45 32 18:30 19:15 33 19:00 Eastbound Westbound

Level ͭ. Building a Simple ScheduleChapter 3. Schedule Building 3-14 Fill in Intermediate Times Now we can start writing trips. Using a spreadsheet this is a very simple process. Just create a depart time, and then use formulas (adding the appropriate running time minutes to the previ- ous cell). Remember that we have entered running times between time points in cells PͲ:Qͮͭ. Cells Q͵ through Qͭͭ contain eastbound running times, while cells Qͭʹ through Qͮͬ contain westbound running times. Using the “show formula” feature of Excel, we enter the following formulas in Row ͳ (eastbound) and Row Ͳ (westbound). For space purposes, eastbound and westbound are shown separately. In the westbound example, formulas in Row Ͳ have been copied to Row ͳ. The formula converts a regularly formatted number to minutes in the time format, as presented earlier. A B C D 0.25 =C7+(0.00069444*$Q$9) =D7+(0.00069444*$Q$10) =E7+(0.00069444*$Q$11) Eastbound D C B A 0.260416666666667 =H6+(0.00069444*$Q$18) =I6+(0.00069444*$Q$19) =J6+(0.00069444*$Q$20) =H6+$Q$35 =H7+(0.00069444*$Q$18) =I7+(0.00069444*$Q$19) =J7+(0.00069444*$Q$20) Westbound 6

Chapter 3. Schedule Building 3-15 Level ͭ. Building a Simple Schedule Formulas can also be used to add trips down the page, but it is easier to copy row ͳ (cells Dͳ: Kͳ) down the page. In fact the whole schedule can be written with just two actual values—the fi rst trip in each direction. The rest will fl ow as formulas. This allows ready manipulation of the trips and schedule, which is a key ally in a scheduler’s arsenal. Using the eastbound direction as an example, the spreadsheet will look like this in “show formula” mode:

Level ͭ. Building a Simple ScheduleChapter 3. Schedule Building 3-16 This example shows the values of the fi lled-in spreadsheet: Since we have said the schedule operates until ͳ:ͬͬ PM, we will take the literal view that this means we provide a last trip at or near that time. That provides a ͳ:ͬͬ PM (ͭ͵:ͬͬ) fi nal trip east- bound and either a Ͳ:Ͱͱ or ͳ:ͭͱ trip westbound. We choose arbitrarily to off er a ͳ:ͭͱ trip. We can partially justify it by being closer to the garage when the trip is over. A B C D E F G H I J K 1 Example Headway Sheet #1 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A 6 6:15 6:26 6:40 6:48 7 6:00 6:08 6:22 6:33 6:45 6:56 7:10 7:18 8 6:30 6:38 6:52 7:03 7:15 7:26 7:40 7:48 9 7:00 7:08 7:22 7:33 7:45 7:56 8:10 8:18 10 7:30 7:38 7:52 8:03 8:15 8:26 8:40 8:48 11 8:00 8:08 8:22 8:33 8:45 8:56 9:10 9:18 12 8:30 8:38 8:52 9:03 9:15 9:26 9:40 9:48 13 9:00 9:08 9:22 9:33 9:45 9:56 10:10 10:18 14 9:30 9:38 9:52 10:03 10:15 10:26 10:40 10:48 15 10:00 10:08 10:22 10:33 10:45 10:56 11:10 11:18 16 10:30 10:38 10:52 11:03 11:15 11:26 11:40 11:48 17 11:00 11:08 11:22 11:33 11:45 11:56 12:10 12:18 18 11:30 11:38 11:52 12:03 12:15 12:26 12:40 12:48 19 12:00 12:08 12:22 12:33 12:45 12:56 13:10 13:18 20 12:30 12:38 12:52 13:03 13:15 13:26 13:40 13:48 21 13:00 13:08 13:22 13:33 13:45 13:56 14:10 14:18 22 13:30 13:38 13:52 14:03 14:15 14:26 14:40 14:48 23 14:00 14:08 14:22 14:33 14:45 14:56 15:10 15:18 24 14:30 14:38 14:52 15:03 15:15 15:26 15:40 15:48 25 15:00 15:08 15:22 15:33 15:45 15:56 16:10 16:18 26 15:30 15:38 15:52 16:03 16:15 16:26 16:40 16:48 27 16:00 16:08 16:22 16:33 16:45 16:56 17:10 17:18 28 16:30 16:38 16:52 17:03 17:15 17:26 17:40 17:48 29 17:00 17:08 17:22 17:33 17:45 17:56 18:10 18:18 30 17:30 17:38 17:52 18:03 18:15 18:26 18:40 18:48 31 18:00 18:08 18:22 18:33 18:45 18:56 19:10 19:18 32 18:30 18:38 18:52 19:03 19:15 19:26 19:40 19:48 33 19:00 19:08 19:22 19:33 Eastbound Westbound

Chapter 3. Schedule Building 3-17 Level ͭ. Building a Simple Schedule With the advent of computerized scheduling, use of the ͮͰ-hour clock, or military time, has become more common and is used in all our examples. Refer to the picture at right if you are not familiar with the ͮͰ-hour clock. Our Simple Schedule in a Computerized Scheduling Package Even if you have access to a computerized scheduling system, it is still important to go through this process. The scheduling system will certainly automate some of the things we’ve discussed—building multiple trips, calculating mileage and hours, and even potentially linking the trips. However, and we cannot stress this enough, the system will only produce quality outputs (i.e., schedules, blocks and runs) if the inputs have been prop- erly developed. “Garbage in, garbage out” is the simplest way to put it. So while it is true that you do not need to build an entire schedule from the start in Excel, it is still important to understand the elements of the scheduling process. Once you have defi ned the route, time points, running times, and distances in your system, trips are easy to create and manipulate. But what time should the trips start? How will the system link? How many buses will we need? These questions need to be asked and answered before any basic schedule is cre- ated. We recommend that you build the schedule pattern just as if you were developing the schedule without a computerized scheduling system (i.e., in a spreadsheet). Just as this process allowed us to create a schedule that would link eff ectively in the spreadsheet, so too will it allow us to create a schedule that links eff ectively in your computerized scheduling system. Even sophis- ticated scheduling packages usually cannot resolve badly written schedules. For example, if we decided to schedule trips depart from “A” at :ͬͬ and :ͯͬ, and from “D” at :ͮͱ and :ͱͱ, such a schedule pattern would result in an additional vehicle whether or not a scheduling package is used. The automated scheduler does off er some inherent capabilities to view obvious issues and work interactively with the schedules. At this point you can begin blocking. As mentioned before we started, we already “know the answer” to how many buses are required before we even do any blocking. We have in fact de- fi ned the schedule to ensure our answer. The next chapter discusses blocking in greater detail.

Level Í­. Building a Simple ScheduleChapter 3. Schedule Building 3-18 LEVEL 1 End of Basic Schedule Building. The Intermediate Section of Schedule Building continues on the next page. To jump to Schedule Blocking, go to page Í°-Í­.

Chapter 3. Schedule Building 3-19 Level ͮ. Intermediate Schedule Building 3.2 A Slightly More Intricate Schedule Let’s continue from where we left off . Again we assume you are building the sched- ule in the spreadsheet, but many of the approaches carry over into computerized scheduling. Suppose you have done a fabulous job of constructing this schedule, just as a good scheduler should, and you have beaten the cost estimate contained in the operating budget. There is enough funding left over to provide additional peak hour service. Peak hours have been defi ned for us as Ͳ:ͬͬ – ͵:ͬͬ AM and ͯ:ͬͬ – Ͳ:ͬͬ PM (ͭͱ:ͬͬ – ͭʹ:ͬͬ). We have some options. (We generally do…that is what makes scheduling seem so daunting for new schedulers.) We could provide a ͭͱ-minute service, which would double the service of the existing schedule, or we could go from our present ͯͬ- to a ͮͬ-minute headway, an approxi- mate ͱͬ% increase in service. Of course, we could provide even better peak service than ͭͱ minutes. Since our remaining service budget is not unlimited, we want to look at both options. This is a very typical task asked of schedulers—“how much will it cost for this frequency, that frequency, or span of service?” Back again to our old friend the Round trip Cycle. To refresh our memory, the minimum ac- ceptable cycle (round-trip running time of ͲͲ minutes plus the prescribed minimum layover) is ͳͯ minutes. To provide a ͮͬ-minute service, look at how multiples of ͮͬ work with that cycle: ͮͬ, Ͱͬ, Ͳͬ, ʹͬ, etc. A cycle of ʹͬ would yield layover of ͭͰ minutes, which is ͮͭ%. Therefore, an increase to ͮͬ–minute service would require one more bus (for a total of four—ʹͬ minutes divided by the ͮͬ-minute headway) in the cycle. For a ͭͱ-minute headway we need to look at multiples of ͭͱ: ͭͱ, ͯͬ, Ͱͱ, Ͳͬ, ͳͱ, ͵ͬ, etc. A ͳͱ- minute cycle would allow for layover of nine minutes, which is acceptable under our contrac- tual requirements (or operating practices, if there is no provision in the contract). But the real question is whether, knowing the practical conditions of traffi c congestion and operating time variability, nine minutes of layover every ͳͱ minutes is enough to reasonably guarantee that buses will recover from delays and leave on time for their next trip. A ͳͱ-minute round trip cycle would require ͱ buses, one more than the ͮͬ minute headway solution, and ͮ more than the initial ͯͬ-minute service proposed. Of course we could also use the ͵ͬ-minute base period cycle, which would preserve the ͭͮ minutes or so at each end of the route, but that would be considered excessive if a better alternative were available. LEVEL 2A When evaluating alter- nate scheduling frequen- cies on a route, always recalculate the round trip cycle time and check the effi ciency of the headway against the cycle. You may fi nd that you can increase service by making the cycle more effi cient. Tip Running “hot” or ahead of schedule is a much more serious problem for riders than running behind schedule. The timetable is essentially a “contract” between the passenger and the transit system that promises that if the passenger arrives at the stop on time the bus will be there to pick them up. Leaving a stop early means that passengers who arrive at the stop on time may have to wait more than an entire headway for the bus to come. Tip

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-20 Let’s now apply a quick rule-of-thumb about costs: the periods of the day when additional buses would operate total about seven hours (two three-hour periods during the morning and afternoon peak periods plus the in and out deadhead time). So, a ͮͬ-minute peak headway would add seven hours, while a ͭͱ-minute peak would add ͭͰ (seven hours x ͮ buses). Apply your system’s cost per hour to that and you get a reasonably accurate cost estimate even be- fore you start building (or in our case, revising) your schedule—again the point of knowing the outcomes before any real schedule writing is undertaken. Which do you choose? The ideal choice is the option that provides the greatest amount of service for which funding is available. But transit systems face the economic problem of unlim- ited wants and limited resources. Therefore we do not want to commit more resources than justifi ed either by the known or the projected ridership—service standards, or your service planners, will be able to assist in making this decision. Then too, there is the concern that peak hour buses add to the ineffi ciency of the schedule in that they require equipment that only gets used for part of the day. They could potentially make for a less effi cient runcut, increasing the number of split runs that will have to be built or ultimately winding up as pieces that cannot be worked into a full run. As you can see, the scheduler is torn between these two positions. In this particular case, the decision has been made to go with the ͭͱ-minute service, as the sys- tem can aff ord it and it off ers a better connection strategy with other routes that operate on a ͯͬ-minute headway (at a ͮͬ-minute headway, this route would miss one of two hourly connec- tions with other ͯͬ-minute routes—this is not a minor consideration). Remembering our round trip cycle calculation, fi ve buses would give us a ͳͱ-minute cycle (we need a minimum of ͳͯ) while six buses would take us to the same ͵ͬ-minute cycle that we currently use during the day for our ͯͬ-minute service. There is no question here. Five buses work within our minimums. We do not need all of the layover we currently apply in the base period. We would cut that down if we could. To create the schedule, we simply insert a few rows during the peaks and add in the extra trips between the schedules—right? But wait. It is not quite as easy as that. You can fi ll in-between trips eastbound beginning with the blank row after Ͳ:ͬͬ under time point “A.” Continue until you reach the ͵:ͬͬ trip. This will add new trips beginning at Ͳ:ͭͱ and continuing at :ͭͱ and :Ͱͱ up to ʹ:Ͱͱ. That will meet the criteria we set for the AM peak period. Beginning with the ͵:ͬͬ trip, we resume our ͯͬ-minute service and can leave these trips just as we wrote them on the fi rst iteration of the schedule. We can do this also for the PM peak period. We add trips between the ͭͱ:ͬͬ and ͭʹ:ͬͬ trips, giving us a solid ͭͱ-minute service for this three hour period, as shown on the following page: split run A run containing two or more pieces of work separated by a break over one hour in length. Also known as a “swing run.” At some systems, three-piece split runs are allowed, but one of the breaks (or “swings”) is usually paid whereas in two-piece split runs the break is generally not paid. Split runs tend to be used to allow both peaks to be covered by one operator since the work day would otherwise be too long for a straight run. pieces Portions of a run, especially distinct portions separated by a break. two-piece run A run made up of two pieces of work separated by an interval of time. The pieces will usually be on different blocks and may be on different routes. three-piece run A run made up of three pieces of work separated by two intervals of time. Generally, one of the intervals in a three-piece run is paid time.

Chapter 3. Schedule Building 3-21 Level Í®. Intermediate Schedule Building Even if your system does not have a required amount of layover, always ask yourself whether the route can be expected to run on time given traffi c conditions and a designated amount of layover. Tip 1 Example Headway Sheet #2 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip Pull In 6:00 6 3 5:55 6:15 6:26 6:40 6:48 7:00 6:30 7 1 5:50 6:00 6:08 6:22 6:33 6:45 6:56 7:10 7:18 7:30 6:15 7:00 8 2 6:20 6:30 6:38 6:52 7:03 7:15 7:26 7:40 7:48 8:00 6:45 7:30 9 3 7:00 7:08 7:22 7:33 7:45 7:56 8:10 8:18 8:30 7:15 8:00 10 1 7:30 7:38 7:52 8:03 8:15 8:26 8:40 8:48 9:00 7:45 8:30 11 2 8:00 8:08 8:22 8:33 8:45 8:56 9:10 9:18 9:30 8:15 9:00 12 3 8:30 8:38 8:52 9:03 9:15 9:26 9:40 9:48 10:00 8:45 13 1 9:00 9:08 9:22 9:33 9:45 9:56 10:10 10:18 10:30 14 2 9:30 9:38 9:52 10:03 10:15 10:26 10:40 10:48 11:00 15 3 10:00 10:08 10:22 10:33 10:45 10:56 11:10 11:18 11:30 16 1 10:30 10:38 10:52 11:03 11:15 11:26 11:40 11:48 12:00 17 2 11:00 11:08 11:22 11:33 11:45 11:56 12:10 12:18 12:30 18 3 11:30 11:38 11:52 12:03 12:15 12:26 12:40 12:48 13:00 19 1 12:00 12:08 12:22 12:33 12:45 12:56 13:10 13:18 13:30 20 2 12:30 12:38 12:52 13:03 13:15 13:26 13:40 13:48 14:00 21 3 13:00 13:08 13:22 13:33 13:45 13:56 14:10 14:18 14:30 22 1 13:30 13:38 13:52 14:03 14:15 14:26 14:40 14:48 15:00 23 2 14:00 14:08 14:22 14:33 14:45 14:56 15:10 15:18 15:30 24 3 14:30 14:38 14:52 15:03 15:15 15:26 15:40 15:48 16:00 25 15:30 1 15:00 15:08 15:22 15:33 15:45 15:56 16:10 16:18 16:30 26 15:15 16:00 2 15:30 15:38 15:52 16:03 16:15 16:26 16:40 16:48 17:00 27 15:45 16:30 3 16:00 16:08 16:22 16:33 16:45 16:56 17:10 17:18 17:30 28 16:15 17:00 1 16:30 16:38 16:52 17:03 17:15 17:26 17:40 17:48 18:00 29 16:45 17:30 2 17:00 17:08 17:22 17:33 17:45 17:56 18:10 18:18 18:30 30 17:15 18:00 3 17:30 17:38 17:52 18:03 18:15 18:26 18:40 18:48 19:00 31 17:45 32 1 18:00 18:08 18:22 18:33 18:45 18:56 19:10 19:18 19:28 33 2 18:30 18:38 18:52 19:03 19:15 19:26 19:40 19:48 19:58 34 3 19:00 19:08 19:22 19:33 19:53 Eastbound Westbound AM peak period The period in the morning when the greatest level of service is provided, typically 6 to 9 AM. PM Peak period The period in the afternoon when the greatest level of service is provided, typically 3 to 7 PM.

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-22 Slipping and Sliding We mentioned the possibility of wanting to “slip or slide” trips before we fi lled in intermediate times. Basically the term relates to moving the trips in one or both directions. We might want to do this for the following reasons: To give more or less layover at one end of the route due to operational reasons, such as the lack of a decent place to park a bus To adjust an intermediate time for a particular reason, such as a positive meet with another route To meet school bell times (in which case we might want to move only one or two trips) Revising this eastbound direction was simple. But this was done without regard to blocking impacts (remember we said—know the answer before you get into the detailed schedule writ- ing). Our previous schedule pattern had ͭͮ minutes of layover at either end, and now we have decided that a total of ͵ minutes per round-trip is going to be applied. We have ͲͲ minutes of running time within a ͳͱ-minute window (ͱ x ͭͱ-minute headway). We can divide the layover equally between both terminals or give more or most to one terminal. It is not wise to give none at all, because that provides no relief valve for late arriving buses. Since this is a theoretical schedule and we really do not know the traffi c conditions at Terminal A versus D, we can pretty much decide our own strategy. So the westbound trips are going to have to move to accommodate the smaller layover we have planned. This is part of the process we call slipping and sliding. Eff ectively we are revisiting the schedule pattern to decide how the peak will work. This raises an important consideration in developing schedules—that the peak schedule pattern may be diff erent from the off -peak schedule pattern. Why? There may be several reasons, including: Diff erent frequencies, a regular occurrence since the bulk of travel is during peak times. Diff erent running times during the day. Running times may change several times dur- ing the day to take into account diff erent operating speeds due to congestion, loads, or other factors. In this example, we continue to assume constant running times all day. The need to have specifi c departure times at specifi c times of day, i.e., to connect with other service or modes whose schedules change at a certain time. To adjust the blocking, perhaps to schedule with less layover during the peaks (to mini- mize peak vehicles), but to allow more time in the off peak where resources aren’t at such a premium. • • • • • • • slipping and sliding The process of shifting one or more trips forward or backward in time to achieve a specifi c purpose. Also known as “trip shifting.” peak vehicles The maximum number of vehicles required to operate the route at the required headway. Quickly calculated as: cycle time divided by headway. Also referred to as “peak vehicle requirement.” base vehicles The number of vehicles required to operate the route at the required headway during the base period. Quickly calculated as: cycle time in the base period divided by headway in the base period. Also referred to as “base period vehicle require- ment.”

Chapter 3. Schedule Building 3-23 Level ͮ. Intermediate Schedule Building In this case we have decided that our preference would be to give three minutes at “D” as the “away” terminal and the remaining six at “A.” Three provides the buff er we are looking for. Re- member that we have done a bang-up job of calculating the running time for accuracy, so we are only concerned with providing that extra buff er for conditions beyond the ordinary. The six minutes at “A” provide a more reasonable time for the operator to get off the bus and stretch his/her legs. We have also decided that we want to keep our existing :ͬͬ and :ͯͬ eastbound departure times (assuming in this case we have a connection we want to make at “A”). Following this strategy means we will have to slide our existing westbound trips earlier by nine minutes, so that the Ͳ:ͬͬ trip arriving at Ͳ:ͯͯ will now leave at Ͳ:ͯͲ instead of the present Ͳ:Ͱͱ. All of this can be looked at as we develop our schedule patterns sheet, which for the AM peak now looks like the following: During the peaks this becomes a ͭͱ-minute repeating schedule pattern. So again our fi rst bus gets back to make the ͳ:ͭͱ departure, giving a ͳͱ-minute cycle. Or to prove the theory, we will need buses for the Ͳ:ͬͬ, Ͳ:ͭͱ, Ͳ:ͯͬ, Ͳ:Ͱͱ and ͳ:ͬͬ eastbound departures (ͱ in all). Some of the above could have been carried out a little diff erently in some computerized sched- uling systems. For example the ability to drag trips along a time distance graph can visually represent the process of creating or altering schedule patterns. It’s pretty simple—move the trip until you see it “fi t” into the linkup. Typically this should be done with one round-trip, eff ec- tively recreating the schedule pattern procedure anyway, before rebuilding the schedule. A B C D E F G H I J K L M 1 Example Headway Sheet #2 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip 8 3 5:50 6:00 6:08 6:22 6:33 6:36 6:47 7:01 7:09 7:15 Eastbound Westbound Some agencies com- bine operator rest time (“layover”) with time to get back on schedule (“recovery”) and others have separate standards and con- tract rules for each. Know the rules of your agency before you begin to schedule! Tip

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-24 Refi ning the Schedule Now we fi ll out the rest of the trips to meet the intended schedule pattern—departures from “A” at :ͬͬ, :ͭͱ, :ͯͬ & :Ͱͱ; departures from “D” at :ͬͲ, :ͮͭ, :ͯͲ & :ͱͭ in the peaks, but keeping midday the same: Transitioning Besides round trip cycles (and accuracy, of course), the most interesting concept to introduce to a new scheduler is transitioning. Transitioning involves the smoothing of the change in head- way, running time, or both. On our fi rst schedule we had the same running time and headway all day, so transitioning was not a factor. This second schedule adds the complication of chang- ing from a ͭͱ-minute during the AM peak to a ͯͬ-minute in the midday, back to a ͭͱ-minute in the PM Peak and fi nally back to a ͯͬ-minute headway during the course of an operating day. The next section will introduce a schedule with variable running time. Learning to smooth these changes is an integral part of being able to develop quality schedules. A B C D E F G H I J K L M 1 Example Headway Sheet #2 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip 6 6:06 6:17 6:31 6:39 6:45 7 6:21 6:32 6:46 6:54 7:00 8 6:00 6:08 6:22 6:33 6:36 6:47 7:01 7:09 7:15 9 6:15 6:23 6:37 6:48 6:51 7:02 7:16 7:24 7:30 10 6:30 6:38 6:52 7:03 7:06 7:17 7:31 7:39 7:45 11 6:45 6:53 7:07 7:18 7:21 7:32 7:46 7:54 8:00 12 7:00 7:08 7:22 7:33 7:36 7:47 8:01 8:09 8:15 13 7:15 7:23 7:37 7:48 7:51 8:02 8:16 8:24 8:30 14 7:30 7:38 7:52 8:03 8:06 8:17 8:31 8:39 8:45 15 7:45 7:53 8:07 8:18 8:21 8:32 8:46 8:54 9:00 16 8:00 8:08 8:22 8:33 8:36 8:47 9:01 9:09 17 8:15 8:23 8:37 8:48 8:51 9:02 9:16 9:24 9:30 18 8:30 8:38 8:52 9:03 9:06 9:17 9:31 9:39 10:00 19 8:45 8:53 9:07 9:18 20 9:00 9:08 9:22 9:33 9:45 9:56 10:10 10:18 10:30 21 9:30 9:38 9:52 10:03 10:15 10:26 10:40 10:48 11:00 22 10:00 10:08 10:22 10:33 10:45 10:56 11:10 11:18 11:30 23 10:30 10:38 10:52 11:03 11:15 11:26 11:40 11:48 12:00 24 11:00 11:08 11:22 11:33 11:45 11:56 12:10 12:18 12:30 25 11:30 11:38 11:52 12:03 12:15 12:26 12:40 12:48 13:00 26 12:00 12:08 12:22 12:33 12:45 12:56 13:10 13:18 13:30 Eastbound Westbound

Chapter 3. Schedule Building 3-25 Level ͮ. Intermediate Schedule Building For our current schedule, we want to review how well we have handled these headway transi- tions. First, look at the end of the AM peak. Notice that eastbound, we abruptly stop providing a ͭͱ-minute service and go directly into a ͯͬ. On a smaller or lighter route, one where policy headways are driving the service strategy, this is perfectly acceptable. If we were driven by demand, there might be a period where the headways would widen (service would reduce) maybe to a ͮͬ, then a ͯͬ-minute headway. However, the service policy is the deciding factor in this case, so we go to the base ͯͬ as soon as our service plan tells us to do so. The westbound side is not so cut and dried, because the leaving times changed to accommo- date the fi ve-bus round trip cycle layover scheme. As the schedule shows, we shift back to the :ͭͱ/:Ͱͱ leave times as we transition out of the peak. Notice that we go from ʹ:ͱͭ to ͵:ͭͱ, which is a ͮͰ-minute headway. That headway is a combination of the ͭͱ- and a nine-minute adjust- ment in order to get the westbound trips onto our three-bus base cycle. It would have been easy to make the next trip ͵:ͬͲ, continuing the ͭͱ-minute headway. But the next trip at ͵:Ͱͱ would have been ͯ͵ minutes later, which is not acceptable when a ͯͬ-minute headway is called for. A similar shift is made going into the PM peak westbound. We move what normally would have been the ͭͱ:ͭͱ trip up (forward) by nine minutes to become the ͭͱ:ͬͲ and the start of our :ͬͲ, :ͮͭ, :ͯͲ and :ͱͭ leaving strategy which puts layover times where we decided earlier we wanted them. You can make these transitions work for you or against you; it is a matter of learning how to do the former. There is no one rule that works every time, because every transition is dif- ferent. But a good scheduler always studies a headway (or running time) transition to see the result. If the result yields a wider headway than you are planning to operate after the change, then you need to look at shifting an earlier trip. In this example, we didn’t want to go from a ͭͱ to a ͯͲ. We could go from a ͭͱ, to a ͮͭ, to a ͯͬ, which is progressively widening the headway. The same situation in reverse is true for shortening the headway going into the PM peak. This is a simple example of transitioning, but its principles hold true even in the most complex schedule. A slightly diff erent approach to the transition from peak to off -peak (and again back to peak) would be to provide a consistent set of departure times westbound throughout the day. This leaves us with a decision—at a ͯͬ-minute headway do we choose :ͬͬ/:ͯͬ or :ͭͱ/:Ͱͱ eastbound, and :ͬͲ/:ͯͲ or :ͮͭ/:ͱͭ westbound? Which to choose may depend on any other connections, at what time you transition to the off peak, or just a general preference. Either would work. In our case we choose :ͬͬ/:ͯͬ eastbound and :ͬͲ/:ͯͲ westbound. This maintains the ͮͰ minutes Transitioning allows service to ease into a new schedule pattern as demand changes gradually over the service day. Tip

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-26 of layover per round-trip, and the three off -peak buses. In eff ect we have revisited the off -peak schedule entirely to keep consistent departure times with the peaks. The off -peak schedule pattern now looks like this: Note that one disadvantage of this approach is that the layover time at point A is now ͮͭ min- utes. Many schedulers would be uncomfortable with this amount of layover, and might choose the fi rst approach to avoid a long layover at one point. Others might tolerate it for the sake of consistent departure times. Now we simply build the schedule according to the schedule pattern. If your formulas are correct (and of course they are!), all intermediate end times will simply adjust. And departure times can be calculated simply by changing the multiplier (or the minutes, if you are using the time function) to ͭͱ (i.e., the trip start time is the previous time plus ͭͱ minutes) during the peaks. For the PM peak begin the ͭͱ-minute schedule at ͭͱ:ͬͬ eastbound and ͭͱ:ͬͲ westbound and continue until the ͭʹ:ͬͬ/ͭʹ:ͬͲ trip. Look at your next trips. They should be six minutes after the arrival time at Point A. Go ahead and add in your Next Trip times for the whole sheet. The fi nal schedule for ͭͱ-minute peak service on Route ͵ͳ under this approach is shown on the next page. As for our simple schedule, the use of a computerized scheduling package will make the re- generation of the schedule much simpler and less prone to error. In this case you could simply delete the westbound trips all at once, keep the existing eastbound, add the new eastbound peak trips, and regenerate the entire westbound schedule, all with relative ease. Use of time/distance and other graphics contained in computerized systems allows a good visual representation of transitioning. Computerized systems also allow the impacts of altered transitioning approaches to be seen immediately (e.g., breaking planned hooks or increasing the number of buses). A B C D E F G H I J K L M 1 Example Headway Sheet #2 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip 20 9:00 9:08 9:22 9:33 9:36 9:47 10:01 10:09 10:30 Eastbound Westbound

Chapter 3. Schedule Building 3-27 Level Í®. Intermediate Schedule Building Transitioning allows service to ease into a new pattern, generally matching service to demand which often changes more gradually over the service day. Tip 1 Example Headway Sheet #2 2 ROUTE 97 Broad Street 3 DAY Weekday 4 5 Block # Pull Out A B C D D C B A Next Trip Block Pull In 6 6:06 6:17 6:31 6:39 6:45 7 6:21 6:32 6:46 6:54 7:00 8 6:00 6:08 6:22 6:33 6:36 6:47 7:01 7:09 7:15 9 6:15 6:23 6:37 6:48 6:51 7:02 7:16 7:24 7:30 10 6:30 6:38 6:52 7:03 7:06 7:17 7:31 7:39 7:45 11 6:45 6:53 7:07 7:18 7:21 7:32 7:46 7:54 8:00 12 7:00 7:08 7:22 7:33 7:36 7:47 8:01 8:09 8:15 13 7:15 7:23 7:37 7:48 7:51 8:02 8:16 8:24 8:30 14 7:30 7:38 7:52 8:03 8:06 8:17 8:31 8:39 8:45 15 7:45 7:53 8:07 8:18 8:21 8:32 8:46 8:54 9:00 16 8:00 8:08 8:22 8:33 8:36 8:47 9:01 9:09 17 8:15 8:23 8:37 8:48 8:51 9:02 9:16 9:24 9:30 18 8:30 8:38 8:52 9:03 9:06 9:17 9:31 9:39 10:00 19 8:45 8:53 9:07 9:18 20 9:00 9:08 9:22 9:33 9:36 9:47 10:01 10:09 10:30 21 9:30 9:38 9:52 10:03 10:06 10:17 10:31 10:39 11:00 22 10:00 10:08 10:22 10:33 10:36 10:47 11:01 11:09 11:30 23 10:30 10:38 10:52 11:03 11:06 11:17 11:31 11:39 12:00 24 11:00 11:08 11:22 11:33 11:36 11:47 12:01 12:09 12:30 25 11:30 11:38 11:52 12:03 12:06 12:17 12:31 12:39 13:00 26 12:00 12:08 12:22 12:33 12:36 12:47 13:01 13:09 13:30 27 12:30 12:38 12:52 13:03 13:06 13:17 13:31 13:39 14:00 28 13:00 13:08 13:22 13:33 13:36 13:47 14:01 14:09 14:30 29 13:30 13:38 13:52 14:03 14:06 14:17 14:31 14:39 15:00 30 14:00 14:08 14:22 14:33 14:36 14:47 15:01 15:09 15:15 31 14:30 14:38 14:52 15:03 15:06 15:17 15:31 15:39 15:45 32 15:21 15:32 15:46 15:54 16:00 33 15:00 15:08 15:22 15:33 15:36 15:47 16:01 16:09 16:15 34 15:15 15:23 15:37 15:48 15:51 16:02 16:16 16:24 16:30 35 15:30 15:38 15:52 16:03 16:06 16:17 16:31 16:39 16:45 36 15:45 15:53 16:07 16:18 16:21 16:32 16:46 16:54 17:00 37 16:00 16:08 16:22 16:33 16:36 16:47 17:01 17:09 17:15 38 16:15 16:23 16:37 16:48 16:51 17:02 17:16 17:24 17:30 39 16:30 16:38 16:52 17:03 17:06 17:17 17:31 17:39 17:45 40 16:45 16:53 17:07 17:18 17:21 17:32 17:46 17:54 18:00 41 17:00 17:08 17:22 17:33 17:36 17:47 18:01 18:09 42 17:15 17:23 17:37 17:48 17:51 18:02 18:16 18:24 18:30 43 17:30 17:38 17:52 18:03 18:06 18:17 18:31 18:39 19:00 44 17:45 17:53 18:07 18:18 45 18:00 18:08 18:22 18:33 18:36 18:47 19:01 19:09 Eastbound Westbound

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-28 Finishing Up Now review your schedule. Does this give us ͭͱ-minute service for the whole of the peak period as defi ned earlier? Is the transition from peak to off -peak and back again the way we want it? If so, we have achieved the results we planned for in our schedule pattern-building exercise. As with the fi rst schedule, take time to look over all aspects of the schedule for completeness and to catch any obvious errors—those things that have changed (or maybe you have failed to change) as the result of the adjustments introduced from the original schedule. That should do it. We now have another schedule ready for the blocking process.

Chapter 3. Schedule Building 3-29 Level Í®. Intermediate Schedule Building LEVEL 2A End of Intermediate Schedule Building, Part A Intermediate Schedule Building, Part B continues on the next page. To jump to Schedule Blocking, go to page Í°-Í­.

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-30 3.3 Working on a More Intricate Schedule Up to this point, new or trial schedules have relied on policy headways and calcu- lated running times for schedule development and construction. Headways and running times are the basic building blocks of all schedules. While they are some- times given to the scheduler, as in the previous exercises, it is often the responsi- bility of the scheduler to build and adjust schedules based on an analysis of pas- senger load data and actual running time information collected by traffi c checkers. As you continue to work your way through this manual, the examples become more complex and introduce new elements of scheduling. In this section, you will learn how to identify po- tential schedule changes based on variations in passenger load and running times. You will also learn to address the need for diff erent running times throughout the day, and how to “smooth” the transition between periods of the day with diff erent running times. Then in the advanced section, put these changes into practice by developing a revised schedule. The schedule in this exercise, for Route ͵Ͳ—Pasco Avenue, is typical of many found on medium to large transit systems. It has headways which vary, both by time of day and direction. It contains running times that also change throughout the operating day. It features multiple service patterns and a larger peak-to-base ratio, meaning that it has a signifi cant peak service that is about Ͱͬ% greater than the amount of service operated during the base period between the peaks. Service then tapers off during the evening period and into late night. A map and the headway sheet for weekday service on Route ͵Ͳ are shown below. LEVEL 2B traffi c checkers Individuals who conduct ride checks or point checks to collect ridership and time-related data. peak-to-base ratio The ratio between the number of buses or trains required to operate the schedule during the higher of the peak periods and by the num- ber of buses in service in the “base” period between the peaks. A peak to base ratio of 2.0 means that twice as many buses are required to operate peak period service as midday service. The peak-to-base ratio greatly infl uences the runcut in terms of the number of straight and split runs that are possible. A higher ratio means more split runs. Even if you are new to scheduling, do not be intimidated by the schedule and all of its detail. Even the most complex schedule can be understood if you review it one portion at a time. Tip Min ot Libby Sand Point Wi sh ram Shelby Es sex Pasco Pasco Pasco Br oa dw ay Rugby Circle Wi llis ton Ha vre 96A 96 Time point Garage ROUTE 96—PASCO AVENUE

Chapter 3. Schedule Building 3-31 Level Í®. Intermediate Schedule Building S C HE D UL E S HE E T Ro u te 96 IN EF F : S eptem ber 15, 2007 M O NDAY T HRU F RIDAY P art 1 NO RTHB O UND S O UTHB O UND OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN BLK GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 5 4:10 4:20 4:28 4:35 4:43 4:53 5:05 1 3:45 4:05 4:18 4:26 4:33 4:41 4:50 4:58 5:05 5:13 5:23 5:35 6 4:55 5:05 5:13 5:20 5:28 5:37 5:49 3 4:05 4:35 4:48 4:56 5:03 5:11 5:20 5:29 5:37 5:47 5:57 6:05 7 4:39 4:59 5:08 5:16 5:23 5:31 5:35 5:44 5:52 6:02 6:12 6:19 5 5:05 5:19 5:29 5:37 5:46 5:50 5:59 6:07 6:17 6:27 6:45 9 4:59 5:19 5:29 5:39 5:47 5:56 6:05 6:14 6:22 6:32 6:42 6:57 1 5:35 5:49 5:59 6:07 6:16 6:20 6:29 6:37 6:47 6:57 7:05 6 5:49 5:59 6:09 6:17 6:26 6:35 6:44 6:52 7:02 7:12 7:17 3 6:05 6:19 6:29 6:37 6:46 6:50 7:01 7:10 7:21 7:32 7:45 7 6:19 6:29 6:39 6:47 6:56 7:05 7:16 7:25 7:36 7:46 7:57 8 5:55 6:25 6:39 6:50 6:59 7:10 7:15 7:26 7:35 7:46 7:57 8:05 4 6:17 6:37 6:49 7:00 7:09 7:20 7:25 7:36 7:45 7:56 8:06 8:23 5 6:45 6:59 7:10 7:19 7:30 7:35 7:46 7:55 8:06 8:17 8:35 9 6:57 7:09 7:20 7:29 7:40 7:45 7:56 8:05 8:16 8:26 8:46 1 7:05 7:19 7:30 7:39 7:50 7:55 8:06 8:15 8:26 8:37 9:05 6 7:17 7:29 7:40 7:49 8:00 8:05 8:16 8:25 8:36 8:46 8:53 10 6:55 7:25 7:39 7:50 7:59 8:10 8:15 8:26 8:35 8:46 8:57 9:17 2 7:17 7:37 7:49 8:00 8:09 8:20 8:25 8:36 8:45 8:56 9:06 9:23 3 7:45 7:59 8:10 8:19 8:30 8:35 8:46 8:55 9:06 9:17 9:35 7 7:57 8:09 8:20 8:29 8:40 8:45 8:56 9:05 9:16 9:26 9:46 8 8:05 8:19 8:30 8:39 8:50 8:55 9:06 9:15 9:26 9:37 9:57 4 8:23 8:34 8:44 8:52 9:02 9:07 9:18 9:27 9:38 9:48 9:53 5 8:35 8:48 8:58 9:06 9:16 9:22 9:31 9:38 9:48 9:59 10:05 6 8:53 9:04 9:14 9:21 9:31 9:37 9:46 9:53 10:03 10:13 10:23 1 9:05 9:18 9:28 9:35 9:44 9:52 10:01 10:08 10:18 10:29 10:35 2 9:23 9:33 9:43 9:50 9:59 10:07 10:16 10:23 10:33 10:43 10:53 3 9:35 9:48 9:58 10:05 10:14 10:22 10:31 10:38 10:48 10:59 11:05 4 9:53 10:03 10:13 10:20 10:29 10:37 10:46 10:53 11:03 11:13 11:23 5 10:05 10:18 10:28 10:35 10:44 10:52 11:01 11:08 11:18 11:29 11:35 6 10:23 10:33 10:43 10:50 10:59 11:07 11:16 11:23 11:33 11:43 11:53 1 10:35 10:48 10:58 11:05 11:14 11:22 11:31 11:38 11:48 11:59 12:05 2 10:53 11:03 11:13 11:20 11:29 11:37 11:46 11:53 12:03 12:13 12:23 3 11:05 11:18 11:28 11:35 11:44 11:52 12:01 12:08 12:18 12:29 12:35 4 11:23 11:33 11:43 11:50 11:59 12:07 12:16 12:23 12:33 12:43 12:53 5 11:35 11:48 11:58 12:05 12:14 12:22 12:31 12:38 12:48 12:59 13:05 6 11:53 12:03 12:13 12:20 12:29 12:37 12:46 12:53 13:03 13:13 13:23 1 12:05 12:18 12:28 12:35 12:44 12:52 13:01 13:08 13:18 13:29 13:35 2 12:23 12:33 12:43 12:50 12:59 13:07 13:16 13:23 13:33 13:43 13:53 3 12:35 12:48 12:58 13:05 13:14 13:22 13:31 13:38 13:48 13:59 14:05 4 12:53 13:03 13:13 13:20 13:29 13:35 13:45 13:52 14:03 14:13 14:23 5 13:05 13:18 13:28 13:35 13:44 13:50 14:00 14:07 14:18 14:29 14:35 6 13:23 13:33 13:43 13:50 13:59 14:05 14:15 14:22 14:33 14:43 14:53

Level Í®. Intermediate Schedule BuildingChapter 3. Schedule Building 3-32 S C HE D UL E S HE E T Ro u te 96 IN EF F : S eptem ber 15, 2007 M O NDAY T HRU F RIDAY P art 2 NO RTHB O UND S O UTHB O UND OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN BLK GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 1 13:35 13:48 13:59 14:06 14:16 14:20 14:30 14:37 14:48 14:59 15:05 2 13:53 14:03 14:14 14:21 14:31 14:35 14:45 14:52 15:03 15:13 15:23 3 14:05 14:18 14:29 14:36 14:46 14:50 15:00 15:07 15:18 15:29 15:35 4 14:23 14:33 14:44 14:51 15:01 15:05 15:15 15:22 15:33 15:43 15:48 5 14:35 14:48 14:59 15:06 15:16 15:20 15:30 15:37 15:48 15:59 16:05 12 15:23 15:33 15:43 15:50 16:01 16:11 16:15 6 14:53 15:03 15:14 15:21 15:31 15:45 15:55 16:02 16:13 16:24 16:32 1 15:05 15:18 15:29 15:36 15:46 15:57 16:07 16:14 16:25 16:35 16:45 2 15:23 15:33 15:44 15:51 16:01 16:09 16:19 16:26 16:37 16:48 16:52 3 15:35 15:48 15:59 16:06 16:16 16:20 16:31 16:39 16:50 17:01 17:05 4 15:48 15:58 16:09 16:16 16:26 16:30 16:41 16:49 17:00 17:12 17:15 11 15:53 16:08 16:19 16:26 16:36 16:40 16:51 16:59 17:10 17:21 17:28 5 16:05 16:18 16:29 16:36 16:46 16:50 17:01 17:09 17:20 17:32 17:36 12 16:15 16:25 16:36 16:44 16:55 17:00 17:11 17:19 17:30 17:41 17:53 13 16:20 16:35 16:46 16:54 17:05 17:10 17:21 17:29 17:40 17:52 18:05 6 16:32 16:45 16:56 17:04 17:15 17:20 17:31 17:39 17:50 18:01 18:21 1 16:45 16:55 17:06 17:14 17:25 17:30 17:40 17:48 17:58 18:10 18:35 2 16:52 17:05 17:16 17:24 17:35 17:40 17:50 17:58 18:08 18:19 18:23 3 17:05 17:15 17:26 17:34 17:45 17:52 18:02 18:10 18:20 18:32 18:52 4 17:15 17:28 17:39 17:47 17:58 18:05 18:15 18:23 18:33 18:44 18:53 11 17:28 17:38 17:49 17:57 18:08 18:18 5 17:36 17:49 17:59 18:06 18:15 18:20 18:30 18:38 18:48 19:00 19:05 12 17:53 18:03 18:13 18:20 18:29 18:35 18:45 18:53 19:03 19:14 19:23 13 18:05 18:18 18:28 18:35 18:44 18:50 18:59 19:06 19:15 19:26 19:35 2 18:23 18:33 18:43 18:50 18:59 19:05 19:14 19:21 19:30 19:40 19:53 1 18:35 18:48 18:58 19:05 19:14 19:25 19:34 19:41 19:50 20:01 20:06 4 18:53 19:03 19:13 19:20 19:29 19:45 19:54 20:01 20:10 20:20 20:28 5 19:05 19:18 19:28 19:35 19:44 19:54 12 19:23 19:33 19:43 19:50 19:59 20:05 20:14 20:21 20:30 20:41 20:46 13 19:35 19:48 19:58 20:05 20:14 20:25 20:34 20:41 20:50 21:00 21:08 2 19:53 20:03 20:12 20:19 20:26 20:36 1 20:06 20:18 20:26 20:32 20:39 20:45 20:54 21:01 21:10 21:21 21:26 4 20:28 20:38 20:46 20:52 20:59 21:05 21:12 21:18 21:26 21:35 21:48 12 20:46 20:58 21:06 21:12 21:19 21:25 21:32 21:38 21:46 21:56 22:06 13 21:08 21:18 21:26 21:32 21:39 21:45 21:52 21:58 22:06 22:15 22:28 1 21:26 21:38 21:46 21:52 21:59 22:05 22:12 22:18 22:26 22:36 22:46 4 21:48 21:58 22:06 22:12 22:19 22:25 22:32 22:38 22:46 22:55 23:08 12 22:06 22:18 22:26 22:32 22:39 22:45 22:52 22:58 23:06 23:16 23:26 13 22:28 22:38 22:46 22:52 22:59 23:05 23:12 23:18 23:26 23:35 23:48 1 22:46 22:58 23:06 23:12 23:19 23:25 23:32 23:38 23:46 23:56 0:06 4 23:08 23:18 23:26 23:32 23:39 23:49 12 23:26 23:38 23:46 23:52 23:59 0:05 0:12 0:18 0:26 0:36 0:56 13 23:48 23:58 0:06 0:12 0:19 0:29 1 0:06 0:18 0:26 0:32 0:39 0:49

Chapter 3. Schedule Building 3-33 Level ͮ. Intermediate Schedule Building Things you need to know for this exercise: ͭ. Ridership on Route ͵Ͳ has been growing, as fi rst revealed by daily farebox passenger boarding fi gures. ͮ. The route has also developed a problem with keeping on schedule. The early warning for this is usually declining on-time performance fi gures. An even more accurate warn- ing may come from the drivers, who let management know they are having trouble keeping the schedule during certain times of the day due to insuffi cient running time and heavy boardings at several locations. The maximum load point (max point for short) has been determined over time for this route from ride checks (see the discussion in Chapter ͮ, Inputs to the Scheduling Process, about ride check analysis). It is at a major intersection, Pasco & Havre, which is also a time point and a fairly sizable transfer point. Route ͵Ͳ has changed character over the years, from a route with a very pronounced peak direction to one where ridership is generally well balanced in both directions during peak periods. This trend has been benefi cial in making better use of sched- uled trips during peaks: previously non-peak-direction trips operated with few passengers but now trips carry good loads in both directions during the peak period. The route has also seen a reduction in peak loads in the peak direction, allowing a slightly wider headway to carry similar numbers of riders per trip. Analysis of trips by time periods provides a sense of how well demand (riders) meets supply (seats plus standees). Schedule departments have traditionally used analysis periods of ͭͱ- to ͯͬ-minute intervals during times when headways are ͭͬ minutes or less and ͯͬ- to Ͳͬ-minute intervals during times when headways are ͭͱ minutes or more. The load average spreadsheet for Route ͵Ͳ is shown on the following page. The load average spreadsheet has thicker lines at hourly intervals during the base and half hourly intervals during the two peaks. We use the scheduled arrival time at the max point (the “due” column, second from the left) to determine where trips fi t in the time breaks. The load analysis examines each time interval. The spreadsheet also contains formulas in each time interval: the fi rst sums all passengers observed (this check collected the maximum number of passengers, whether that was the arriving load or the leaving load); the second calculates the average load per trip within the time interval. Average load per trip within the time interval is shown in bold on the load average spreadsheet. The most productive transit routes are those that have balanced demand in both directions. Routes with a very pronounced peak direction may be very full in one direction, but must return with very light loads to recycle. Designing routes to serve important nodes on both ends will generally improve productivity. Tip

Level Í®. Intermediate Schedule BuildingChapter 3. Schedule Building 3-34 peak of the peak The absolute busiest time interval (measured in short increments such as 15 or 30 minutes, depending on headway) during the peak period, in terms of passenger demand and service. S A M P LE TRA NS IT A GE NC Y AVE R AG E D MAX LO AD P O IN T C H E C K S RO UT E 96 - P AS CO AV ENUE W EEKDAY S CHED NO . 5 S O UT HBO UND P AS CO & HAV RE ARRIV ING L O AD Tues day A pril 1 Thurs day A pril 10 W ednes day M ay 7 S unny 47 degrees Cloudy , ra in, 54 degrees O verc as t, c ool, 57 degrees BL K DUE ACT UAL L O AD T o t/Avg ACT UAL L O AD T o t/Avg ACT UAL L O AD T o t/Avg AV ERAG E 5 6:07 6:08 11 6:09 14 6:06 12 9 6:22 6:23 27 6:22 30 6:22 26 1 6:37 6:37 22 88 6:38 24 97 6:39 23 87 6 6:52 6:51 28 22 6:55 29 24 6:53 26 22 23 3 7:10 7:10 33 69 7:09 35 70 7:12 31 64 7 7:25 7:26 36 35 7:26 35 35 7:26 33 32 34 8 7:35 7:36 38 7:38 37 7:37 39 4 7:45 7:42 41 123 7:46 43 126 7:46 40 121 5 7:55 7:58 44 41 7:58 46 42 7:58 42 40 41 9 8:05 8:07 40 8:05 43 8:06 41 1 8:15 8:16 42 120 8:16 43 126 8:15 40 117 6 8:25 8:27 38 40 8:28 40 42 8:24 36 39 40 10 8:35 8:35 36 8:35 37 8:37 33 2 8:45 8:46 32 102 8:45 35 104 8:46 33 96 3 8:55 8:57 34 34 8:56 32 35 8:55 30 32 34 7 9:05 9:04 27 9:06 33 9:05 30 8 9:15 9:26 40 9:15 27 9:16 25 4 9:27 9:27 14 9:28 26 9:28 24 5 9:38 9:41 23 130 9:40 24 132 9:41 21 124 6 9:53 9:54 26 26 9:55 22 26 9:53 24 25 26 1 10:08 10:07 21 10:08 23 10:08 22 2 10:23 10:23 19 10:24 22 10:25 20 3 10:38 10:37 22 80 10:37 23 90 10:40 23 83 4 10:53 10:55 18 20 10:53 22 23 10:54 18 21 21 5 11:08 11:08 24 11:10 29 11:08 27 6 11:23 11:25 26 11:23 24 11:23 25 1 11:38 11:37 25 101 11:39 25 106 11:38 24 102 2 11:53 11:53 26 25 11:58 28 27 11:55 26 26 26 3 12:08 12:08 23 12:09 25 12:09 26 4 12:23 12:24 25 12:20 15 12:24 27 5 12:38 12:40 24 100 12:38 36 105 12:38 23 104 6 12:53 12:54 28 25 12:54 29 26 12:53 28 26 26 1 13:08 13:08 28 13:08 30 13:08 29 2 13:23 13:23 27 13:24 29 13:24 26 3 13:38 13:39 32 106 13:39 31 115 13:39 29 106 4 13:52 13:50 19 27 13:53 25 29 13:54 22 27 27 5 14:07 14:07 33 14:08 35 14:09 32 6 14:22 14:24 28 14:22 32 14:22 28 1 14:37 14:34 22 110 14:37 33 136 14:40 29 121 2 14:52 14:50 27 28 14:55 36 34 14:53 32 30 31 3 15:07 15:07 29 15:07 31 15:06 30 4 15:22 15:22 28 15:22 30 15:23 29 5 15:37 15:39 31 120 15:36 32 127 15:37 27 116 14 15:50 15:53 32 30 15:50 34 32 15:54 30 29 30 6 16:02 16:01 36 16:04 38 16:04 35 1 16:14 16:15 34 109 16:15 37 116 16:14 29 97 2 16:26 16:28 39 36 16:28 41 39 16:27 33 32 36 3 16:39 16:41 38 16:38 40 16:41 42 4 16:49 16:49 43 128 16:50 46 135 16:51 44 136 12 16:59 17:01 47 43 17:00 49 45 17:00 50 45 44 5 17:09 17:13 51 17:10 55 17:09 54 13 17:19 17:22 53 153 17:21 58 166 17:20 56 164 14 17:29 17:32 49 51 17:31 53 55 17:33 54 55 54 6 17:39 17:43 44 17:42 48 17:41 49 1 17:48 17:48 39 118 17:48 40 130 17:47 41 127 11 17:58 17:58 35 39 17:58 42 43 17:58 37 42 42 3 18:10 18:11 30 18:10 37 18:11 33 2 18:23 18:24 27 18:25 32 18:25 30 4 18:38 18:39 29 110 18:39 30 127 18:39 26 118 13 18:53 18:53 24 28 18:53 28 32 18:54 29 30 30 14 19:06 19:07 20 19:09 28 19:06 24 6 19:21 19:20 18 53 19:22 20 68 19:22 19 60 1 19:41 19:41 15 18 19:42 20 23 19:41 17 20 20 2 20:01 20:02 19 20:01 22 20:02 20 13 20:21 20:21 12 47 20:23 16 56 20:21 15 54 14 20:41 20:40 16 16 20:40 18 19 20:43 19 18 17 1 21:01 21:01 11 21:01 15 21:00 12 2 21:18 21:19 9 21:18 12 21:18 14 13 21:38 21:39 14 44 21:42 13 51 21:39 11 49 14 22:01 22:01 10 11 21:59 11 13 21:59 12 12 12 Peaks of the peak loads

Chapter 3. Schedule Building 3-35 Level ͮ. Intermediate Schedule Building Route ͵Ͳ operates past the maximum load point every ͭͱ minutes during the base period and every ͭͬ during the peaks. So the peak periods are divided into ͯͬ-minute intervals and the base period into Ͳͬ-minute intervals. The time interval is critical. We do not want to miss the high peak of the peak loads by averag- ing these with too many trips on either side (in the shoulders of the peak). We cannot always schedule eff ectively for the peak of the peak demand, but averaging trips that are too far away from the peak of the peak can give us a false lower estimation of peak demand. Use of a ͯͬ- minute interval during the peak periods avoids this pitfall on Route ͵Ͳ. Keep in mind the overall purpose, which is to be able to compare observed loads against es- tablished service standards. Looking at individual trip loadings is too precise for analysis when service is this frequent, as trips can run erratically due to traffi c and other factors largely out of the control of the transit system. These factors can produce overloads on one trip while sur- rounding trips are running with fewer passengers than normal. Bus operators also vary as to style of driving. Some are faster than others, meaning they are able to handle the business of collecting fares, handing out information, tying down wheelchairs, and maneuvering through traffi c better than their fellow operators. The averaging process within the analysis period helps to compensate for these diff erences. The average load spreadsheet is laid out to accommodate three separate days’ checks. We could add or subtract columns based on the number of days of data available. As always, more than one day of data is recommended for any schedule analysis. For this example, we concentrate on the maximum load point of the route for data collection. Route ͵Ͳ has two branches, designated ͵Ͳ and ͵ͲA on the driver’s route map, although ͵ͲA may not appear on public timetables or bus headsigns.ͭ A thorough review of ridership would also call for a point check at the junction of these two branches, at the time point of Pasco & Essex. The existing schedule is built with all trips alternating between each branch throughout the day. This is the most practical arrangement when route branches exist, but it does not mean that ridership justifi es this equal distribution of service. One branch could be signifi cantly weaker and only justify, say, one out of three trips. Since the balance of ridership between the two branches usually does not change much over time, it is not necessary to schedule point checks at this location on a regular basis. For the purpose of this exercise, ridership on each branch is assumed to be roughly equal and checks made at Pasco & Essex have shown very little shift over the past several years. Even if you have the resources for trip-by-trip analysis, traffi c check data should be averaged over a time interval of three to four times the headway. Loading on individual trips varies greatly, while loading over a time period remains fairly constant. Tip 1 Schedules material will often contain notations for operating personnel—including telephone information for customer service representatives—that do not appear on written public materials. Identifying the branch of a route (such as the 96A in our example) for operational purposes, but not for the public, is not uncommon.

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-36 With all load numbers laid out conveniently on this sheet, it is easy to see the dimensions of the peak. During the AM peak in the southbound direction, service levels are adequate. On average, there are two to three standees per trip between ͳ:ͯͬ and ʹ:ͬͬ AM (average load is Ͱͭ) and between ʹ:ͬͬ and ʹ:ͯͬ AM (average load is Ͱͬ). We would then want to look at the northbound direction loads, the known peak direction, before making any judgment on service adjustments. In the PM, it is a diff erent situation. For the ͭͳ:ͬͬ-ͭͳ:ͯͬ peak half hour, the average load is ͱͯ, fi ve higher than the standard allows. The time periods before and after this period show aver- ages of Ͱͮ and ͰͰ, respectively, which are within the standard. An additional trip is needed in this half-hour period in order to bring the loads down to within the maximum specifi ed in the standard (Ͱʹ). A simple calculation shows that a fourth trip during this half hour would bring the average load down to slightly more than ͯ͵. Since the neighboring time intervals could benefi t from the added trip, we would extend the reduced headway for more than just the peak half-hour period. It is a good idea to sketch any potential change to see what the proposed schedule might look like. Here is an initial proposal for fi xing the overload period: Southbound times at the max point (Pasco & Havre): Present Proposed 16:39 16:39 16:49 16:48 16:59 16:56 17:04 17:09 17:12 17:19 17:20 17:29 17:28 17:39 17:37 17:48 17:47 This particular adjustment spreads the benefi t of the additional trip over an approximate Ͱͬ- minute period, which helps to lower the peak count on six trips. What other eff ects does this have on the schedule? The scheduler knows that the layover at both ends of the route is already tight, so it is unlikely that this extra trip can be provided using the existing number of buses. But it is too early in the process to fi nalize this change. The scheduler also noted that The amount of data available for analysis will depend both on the number of days of checking and on the schedule used to deploy traffi c checkers. Traffi c checking shifts can be scheduled in different ways. A typical checking assignment will cover a location for 16 straight hours with two shifts, often 5:00 AM to 9:00 PM or 6:00 AM to 10:00 PM. These shifts cover the times when there is usually the great- est need to observe loads and trip performance. At times there may be a need to look at the ends of the service day. In this case, a “start to fi nish” schedule, which will typically leave a portion of the middle of the day uncovered, can be used. For Route 96, the early checker would be in place at Pasco & Havre at about 4:25 AM and remain there until 12:25 PM. The afternoon checker would be assigned there at least by 4:30 PM and remain there until the last trip, a northbound bus, passes at 12:26 AM. Combin- ing both of these types of checks together provides the whole picture on max point ridership. One fi nal point on scheduling traffi c checks is that checkers, like all em- ployees, will need breaks for meal times and rest periods. Check- ing over multiple days can allow checker breaks to occur at different times on different days, ensuring that there are no signifi cant gaps in data collection. Tip

Chapter 3. Schedule Building 3-37 Level ͮ. Intermediate Schedule Building most of the trips in the peak, as well as during other times in the operating day, seem to be ar- riving late. A running time analysis is appropriate before crafting a fi nal change proposal. Before analyzing the running time, the scheduler needs to examine the base and evening periods. Diff erent standards are provided for those periods. During the base, the agency’s standards call for a minimum ͱͬ% load during the midday period and all day on Saturday. This guideline is meant to allow for a better base service frequency, which is expected to attract more riders. That translates to a half seated load of at least ͭ͵ on each trip. The hourly time analyses between ͵:ͬͬ AM and Ͱ:ͬͬ PM (ͭͲ:ͬͬ) all exceed that, ranging from ͮͭ to a high of ͯͬ just before the shoulder of the PM peak. The scheduler could actually look at the eff ect of add- ing some base service. The passengers per-minute (PPM) calculation helps here, providing a quick way of performing a what-if analysis. How is the PPM fi gure calculated? The following example using the average loads of the three ridechecks on Route ͵Ͳ illustrates the calculation during the peak of the peak just after ͱ:ͬͬ PM. Trip Arrive Load Minutes since last trip Trip PPM Minutes since 16:49 Period PPM 16:49 0 0 16:59 49 10 4.90 10 4.90 17:09 53 10 5.30 20 5.10 17:19 56 10 5.60 30 5.27 17:29 52 10 5.20 40 5.23 Total 214 How many passengers should be on each bus? If the service standards call for a seated load plus a ͮͱ% standee rate during the peak period (a common standard) and the buses assigned to this route seat ͯʹ, then each trip should be scheduled to carry a maximum of Ͱʹ passengers past the max point. In this example, all four trips exceed a load of Ͱʹ. At Ͱ.͵ PPM for the ͭͲ:ͱ͵ trip, if the bus were only one minute earlier, there would be ͰͰ instead of Ͱ͵ patrons on board. Since the PPM can be highly volatile, especially when the service is running erratically, it is easier to “smooth” out the calculation by looking at a number of trips over time. For the entire passengers per-minute or PPM for short, is the measure- ment of how many people accumu- late every minute at all bus stops waiting for service in the direction being analyzed. It is generally expressed as a decimal number, such as 5.8 PPM. What that means is that, between the time the last trip departed and the next trip is at the stop, 5.8 potential customers arrive at this bus stop every minute. That number helps tell us how much service we need to run to meet the demand within our service standard.

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-38 Ͱͬ-minute time period we have analyzed, the PPM is ͱ.ͮͯ. Divided into a Ͱʹ minute cycle time, we fi nd that a nine-minute headway would provide the service level we are looking for. It is also useful if we decide to adjust loads on our sheet to account for early and late trips. To keep our discussion of max point analysis a bit simpler, we will “eyeball” the early or late trips, their corresponding loads, and mentally make adjustments as we record averages by time period. This practice is certainly acceptable provided that we know our route and a little about what causes early or late operation. If the max load numbers are accurate (and they are by this point), then our judgment should not cause us to err signifi cantly in producing a representative average for the time period. We can take the noon hour, where the average load is ͮͲ and calculate what would happen if we went from four to fi ve buses per hour (a ͭͮ-minute headway on the trunk portion of the route). We have a three-day average of ͭͬͯ passengers over a Ͳͬ-minute time period, which yields a PPM of ͭ.ͳͮ. Multiplying that number by ͭͮ (the new headway) gives us ͮͭ, the num- ber of average passengers on-board for the improved service. Since our goal is to have no fewer than ͭ͵ on board, a ͭͮ-minute headway would meet our goal. We know we need to add PM peak service and we could also add some service in the base, but the base addition is discretionary. The current average load of ͮͲ represents only Ͳʹ% of the seats fi lled and no standees. The following considerations will infl uence the decision: Can the agency aff ord the additional Ͳ-ͭͮ platform hours that one or two added buses would cost us? Does the ridership trend in the base on this route continue to show growth? Is the average load in any of the time periods approaching a seated load? Is the peak-to-base ratio on this route high enough to justify more base service in order to help produce a more economical runcut? The last two points are the most germane in helping to make the decision. The average loads are not high enough to be a concern at this point and the peak-to-base ratio is still reasonable (six base buses compared with ͭͬ during the peak, giving a ratio of ͭ.Ͳͳ). Anything below a ratio of ͮ.ͬͬ will produce a reasonably cost-effi cient runcut in most situations. (More on what makes a runcut cost-effi cient is presented in Chapter ͱ.) The decision, then, is to adjust the PM peak service to address the overloads and leave the base period alone for now. The next step is analyzing running time. • • • •

Chapter 3. Schedule Building 3-39 Level ͮ. Intermediate Schedule Building When planning peak hour service, it is often useful to have standards that refl ect the maximum number of people that should be on board the bus at the maximum load point. Higher loads will result in increased ser- vice. For off-peak service, includ- ing evenings and weekends, it is useful to have both maximum load standards and standards that refl ect the minimum number of passengers that should be on board before service is reduced. Tip Running Time Checks Running time is even more volatile than passenger loads since it depends on street conditions, and individual driver habits. To account for variations in running time, schedulers should err on the side of having more checks available to analyze. Ride checks can be taken continuously throughout the system and, like point checks, can be supplemented with regular discussions with drivers and other operating personnel who are known to give accurate feedback. The early warning mechanism in this example is noting that a number of the trips on Route ͵Ͳ showed up late at the maximum load point. Also, there were no more than a handful of early trips, which is an indicator that running time suffi ciency needs to be reviewed. For this pur- pose, the scheduler once again turns to a three-day check summary. The most effi cient way of obtaining a multi-day summary of running time data is from automated data collection meth- ods, such as APCs or an AVL system. But not all transit properties have APCs or have plans to procure them in the near future. What are the best manual methods of spreading and calculating running times? There are two basic steps in this task. First is the analysis of individual checks. This includes a review of the check itself for normalcy of operation and for possible hand adjustment to account for any slightly erratic operation so that the times will refl ect what would be considered the “normal case” if the aberrations were removed. Once the “normal” or “representative” checks are accumulated and the “outlier” checks have been discarded, the second step is to post the times to a comparison sheet where the multiple days’ checks can be readily studied and averaged. The example on page ͯ-ͯ͵ shows a portion of an expanded headway sheet that could be marked up manually or fi lled in electronically, complete with formulas to average the several days’ observed running times. These times have been analyzed beforehand, so no additional notations or allowances need to be made. The spreadsheet has two columns beside the observed running time totals that show the pres- ent running time period breaks and the scheduled running time. The bold horizontal lines mark the beginning and end of periods for which running times will be averaged. Three-day averag- es of running times for each trip in each direction are shown in the columns to the right of the northbound and southbound schedules. Next, the recommended (or “decided”) running times for a given time period are displayed.

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-40 Establishing Running Time Periods There are two separate steps in analyzing running time: ͭ. Break the operating day down into individual running time periods for each direction ͮ. Analyze and adjust the individual running times between time points so they add up to the total for the one-way trip. Running time periods, also called “classes,” “breaks,” and “levels” at various systems, are times of the day when a specifi c running time is in eff ect. The number for each schedule can vary from one running time period for the entire day to ͮͬ or more. They are established or adjusted by looking at trends in how total trip running times vary over the day. Total one-way running times have traditionally been used to fi nd where these breaks occur, as the individual times between time points provide too much information to digest and consider manually. Comput- erized scheduling packages simplify the adjustment of running times by segment. We begin by looking at the total running time for each trip in each direction. We are trying to spot trends. Running times tend to jump around a bit. In the example below, note that even with the variances you can see when the trend is moving upward or downward.

Chapter 3. Schedule Building 3-41 Level ͮ. Intermediate Schedule Building Trip Total Time 5:06 42 5:26 44 5:40 43 5:55 46 6:10 49 6:20 48 6:20 51 6:40 49 6:50 50 7:00 53 7:10 55 7:20 54 7:30 56 7:40 55 7:50 54 8:00 55 8:10 53 8:20 51 8:35 49 8:50 48 9:05 50 9:25 47 9:45 46 10:05 47 The fi gures represent total trip times during the early morning, AM peak, and mid morning base periods. On fi rst glance, it looks as if there is no order at all to totals, much less a trend. But experience suggests that even with some slight variations among adjacent trips, the trend should be for increases during the buildup to the ʹ:ͬͬ AM peak-of-the-peak and decreases afterward.

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-42 The fi rst three trips are all within a minute of an average Ͱͯ minutes of running time. The running time for the fourth trip at ͱ:ͱͱ is notably higher, so a time break before the ͱ:ͱͱ trip is appropriate. Likewise, there is a similarity in running times between ͳ:ͬͬ and ʹ:ͭͬ. The times range between ͱͯ and ͱͲ minutes and average ͱͰ.Ͱ minutes. Toward the end of the table in the base period, running time is in the ͰͲ to Ͱͳ minute range. The average of the last three trips on our table is Ͱͳ. Thus, we have dealt with the easier-to-spot areas fi rst. Between the early trips and the peak and between the peak and the base are transition areas. Times either ramp up or down relatively quickly. The question is: how big is the gap between the highest peak number and the lowest early or base number? Can one transitional running time bridge the gap or is the diff erence large enough to require two or more running time periods? Following is the same table of trip times sliced into diff erent running time periods using the method just described.

Chapter 3. Schedule Building 3-43 Level ͮ. Intermediate Schedule Building Trip Total Time Average 5:06 42 5:26 44 43 5:40 43 5:55 46 6:10 49 6:20 48 6:20 51 48.8 6:40 49 6:50 50 7:00 53 7:10 55 7:20 54 7:30 56 54.4 7:40 55 7:50 54 8:00 55 8:10 53 8:20 51 8:35 49 49.5 8:50 48 9:05 50 9:25 47 9:45 46 47 10:05 47 The transition period from the early AM to the AM peak must help bridge an increase of ͭͭ minutes. Analysis of the actual trip times shows a range from ͰͲ to ͱͭ minutes during the tran- sition period between ͱ:ͱͱ and Ͳ:ͱͬ. The average of all six trips is Ͱʹ.ʹ rounded to Ͱ͵, about halfway between the adjacent averages. In this case, the decision is to go with the Ͱ͵ and just one transition running time period.

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-44 An alternate but equally reasonable choice would have been to divide the period into two three-trip periods. Under this option, the fi rst three trips average Ͱͳ, while the second three average ͱͬ. The result would be two transitional running time periods and a better smoothing (in terms of less headway variation) of the running time transitions. Either one or two transition running time periods is acceptable, so long as the scheduler plans to perform manual smooth- ing of the trips to keep headways as close to ͭͬ minutes as possible. The second transition, into the base, is less dramatic, having a diff erence of only seven min- utes. One transitional running time period should suffi ce here and the times average ͱͬ, which is just about halfway between the two times. A similar eff ort, not shown here, is needed going into and out of the PM peak. From the PM peak into the night running time, two transition periods might be needed because of the large drop in running time. This same principle applies to our large running time summary sheet for Route ͵Ͳ. The fi rst step is to “eyeball” the totals on the sheet, looking especially at the peaks and valleys during the day. Then group similar running time totals into periods. Laying out individual running time observations this way provides an ideal way of looking at trends. As noted earlier, the spread- sheet has two columns beside the observed running time totals that show the present run- ning time period breaks and the scheduled running time. Working on the computer or on hard copies of these sheets, the scheduler can make notations about any needed changes , both to the time when running time periods change and to new, proposed totals. Note again that the scheduler works fi rst with totals and then works backwards to adjust the individual running times. The analysis of the AM peak generally shows the present running times are adequate. Individu- al times on trips and trip segments do vary, but over the full period of the peak, actual running times are very close to scheduled running times for each branch in both the northbound and southbound directions. The same holds true of the base.

Chapter 3. Schedule Building 3-45 Level Í®. Intermediate Schedule Building HE AD W A Y S HE ET L i n e 96 IN EFF : S eptem ber 15, 2007 M O NDA Y T HRU F RIDA Y H E A D W A Y W ITH 3 -D A Y RUNN IN G TIM E C H E C K S A D D E D DIRE CTIO N = NO RTH - S O UTH A M Libby Sand Pasco Pasco Pasco Rugby Avg Avg Proposed Proposed Rugby Pasco Pasco Pasco Sand Libby IN Avg Avg Proposed Proposed Wishrm Point Essex Havre Willis Circle Lib/Wsh Sand Pt Lib/Wsh Sand Pt Circle Willis Havre Essex Point Wishrm GAR Lib/Wsh Sand Pt Sand Pt Lib/Wsh 5:05 5:19 5:29 5:37 5:46 5:50 5:59 6:07 6:17 6:27 5:19 5:29 5:39 5:47 5:56 6:05 6:14 6:22 6:32 6:42 9.5 8 9 10 10 7.5 9.5 9 9 7.5 10 9 9.5 7.67 9.5 9.33 36 5:35 5:49 5:59 6:07 6:16 6:20 6:29 6:37 6:47 6:57 37 37 9 8 10 9.5 8.5 8.5 9.5 9.5 9.5 8 11 10 9 8.17 10 .2 9.67 37 5:49 5:59 6:09 6:17 6:26 6:35 6:44 6:52 7:02 7:12 41 37 9.5 8 10 10 8.5 9 9.5 9.5 9.5 9 9.5 9.5 9.17 8.67 9.67 9.67 37 6:05 6:19 6:29 6:37 6:46 6:50 7:01 7:10 7:21 7:32 14 9.5 8 9.5 10 9 10 11 13 9.5 8.5 9.5 10 .5 9.5 11 11 .5 13 .5 10 8 9 10 .5 9.5 11 10 .5 13 .5 9.67 8.17 9.33 41 10 .3 9.33 10 .7 11 41 6:19 6:29 6:39 6:47 6:56 7:05 7:16 7:25 7:36 7:46 10 9.5 8.5 9 11 9 10 10 10 10 9 9.5 10 .5 8.5 11 9 9.5 10 .5 8.5 9.5 10 .5 9 11 .5 12 9.83 10 8.67 9.33 38 10 .7 8.83 10 .8 10 .3 41 6:25 6:39 6:50 6:59 7:10 7:15 7:26 7:35 7:46 7:57 13 12 9 10 11 .5 9 11 11 14 11 8 11 11 9 12 10 14 11 9 12 11 8 11 10 13 .7 11 .3 8.67 11 45 11 .2 8.67 11 .3 10 .3 42 6:37 6:49 7:00 7:09 7:20 7:25 7:36 7:45 7:56 8:06 11 12 9 11 11 9 11 10 41 42 12 11 9 12 12 9 10 10 12 12 8 11 11 10 11 11 11 .7 11 .7 8.67 11 .3 43 11 .3 9.33 10 .7 10 .3 42 6:45 6:59 7:10 7:19 7:30 7:35 7:46 7:55 8:06 8:17 14 11 9 12 11 9 12 11 14 11 10 11 11 9 11 12 15 11 9 11 12 10 11 11 14 .3 11 9.33 11 .3 46 11 .3 9.33 11 .3 11 .3 43 6:57 7:09 7:20 7:29 7:40 7:45 7:56 8:05 8:16 8:26 8:46 12 11 9 11 10 9 11 10 13 10 8 11 45 43 11 8 10 11 11 11 9 12 11 9 11 11

Level Í®. Intermediate Schedule BuildingChapter 3. Schedule Building 3-46 A look at the PM peak shows the inadequacy noted earlier based on the analysis of the passen- ger load checks at the max point. More than a few trips arrived late at Pasco & Havre by one or two minutes. At the same time, overcrowding was seen on southbound trips during the height of the PM peak. These two trends suggest the need to rebuild the PM portion of the schedule. H E A D W A Y S H E E T L in e 9 6 IN EFF : S ep te m be r 15 , 200 7 M O NDA Y T HRU F R IDA Y HE AD W A Y W ITH 3-D A Y RUNNING TIME C HE C K S A D D E D D IR E C TIO N = N O R TH - S O U TH P M P E A K P E R IO D Libby Sand Pasco Pasco Pasco Rugby Avg Avg Proposed Proposed Rugby Pasco Pasco Pasco Sand Libby Avg Avg Proposed Proposed Wishrm Point Essex Havre Willis Circle Lib/Wsh Sand Pt Lib/Wsh Sand Pt Circle Willis Havre Essex Point Wishrm LVE. Lib/Wsh Sand Pt Sand Pt Lib/Wsh 15 :3 5 15 :4 8 15 :5 9 16 :0 6 16 :1 6 16 :2 0 16 :3 1 16 :3 9 16 :5 0 17 :0 1 17 :0 5 13 12 7 10 12 9 12 12 12 11 7 11 12 9 11 12 13 12 7 10 13 8 12 13 12.7 11.7 7 10.3 42 12.3 8.67 11.7 12.3 45 15 :4 8 15 :5 8 16 :0 9 16 :1 6 16 :2 6 16 :3 0 16 :4 1 16 :4 9 17 :0 0 17 :1 2 17 :1 5 11 11 7 10 13 9 13 13 4 5 4 6 10 11 8 9 12 8 12 13 11 10 8 10 11 9 12 13 10.7 10.7 7.67 9.67 39 12 8.67 12.3 13 46 16 :0 8 16 :1 9 16 :2 6 16 :3 6 16 :4 0 16 :5 1 16 :5 9 17 :1 0 17 :2 1 17 :2 8 12 7 10 12 9 12 12 11 7 11 13 9 12 13 11 8 10 12 8 11 13 11.3 7.33 10.3 29 12.3 8.67 11.7 12.7 45 16 :0 5 16 :1 8 16 :2 9 16 :3 6 16 :4 6 16 :5 0 17 :0 1 17 :0 9 17 :2 0 17 :3 2 17 :3 6 13 12 7 10 12 8 12 13 13 11 8 10 12 9 13 14 14 12 8 10 11 8 12 13 13.3 11.7 7.67 10 43 11.7 8.33 12.3 13.3 46 16 :1 5 16 :2 5 16 :3 6 16 :4 4 16 :5 5 17 :0 0 17 :1 1 17 :1 9 17 :3 0 17 :4 1 17 :5 3 11 12 8 10 12 8 12 12 11 12 8 11 4 5 4 2 11 9 13 12 10 11 9 11 13 9 12 11 10.7 11.7 8.33 10.7 41 12 8.67 12.3 11.7 45 1 6 : 3 5 1 6 : 4 6 1 6 : 5 4 1 7 : 0 5 17 :1 0 17 :2 1 17 :2 9 17 :4 0 17 :5 2 18 :0 5 12 8 11 12 9 12 13 12 8 10 12 8 11 13 4 5 4 6 12 7 11 13 8 12 14 12 7.67 10.7 30 12.3 8.33 11.7 13.3 46 16 :3 2 16 :4 5 16 :5 6 17 :0 4 17 :1 5 17 :2 0 17 :3 1 17 :3 9 17 :5 0 18 :0 1 14 12 8 11 12 9 11 13 13 11 7 12 13 8 12 12 13 11 7 11 12 8 12 11 13.3 11.3 7.33 11.3 43 12.3 8.33 11.7 12 44 16 :4 5 16 :5 5 17 :0 6 17 :1 4 17 :2 5 17 :3 0 17 :4 0 17 :4 8 17 :5 8 18 :1 0 18 :3 5 11 11 7 11 4 5 4 2 12 8 11 13 11 12 8 11 12 9 12 12 11 12 8 10 11 8 11 11 11 11.7 7.67 10.7 41 11.7 8.33 11.3 12 43

Chapter 3. Schedule Building 3-47 Level ͮ. Intermediate Schedule Building A sketch of proposed headway changes (refer back to page Ͱͯ) indicated that an eight-min- ute headway in the peak of the peak would meet the load standard. The tables below show a comparison of present versus proposed adjusted running times. On these tables, the start time of the fi rst trip with a change in running time is highlighted in gray to allow the reader to refer back to the original schedule. NORTHBOUND Current Runtimes Proposed Runtimes Period Beginning Wishram Sand Point Period Beginning Wishram Sand Point Ͱ:ͬͬ ͯͲ ͯͮ Ͱ:ͬͬ ͯͲ ͯͮ ͱ:ͬͱ Ͱͭ ͯͳ ͱ:ͬͱ Ͱͭ ͯͳ Ͳ:ͮͱ Ͱͱ Ͱͯ Ͳ:ͮͱ Ͱͱ Ͱͯ ʹ:ͮͯ Ͱͭ ͯ͵ ʹ:ͮͯ Ͱͭ ͯ͵ ʹ:ͱͯ ͯ͵ ͯʹ ʹ:ͱͯ ͯ͵ ͯʹ ͵:ͮͯ ͯ͵ ͯͲ ͵:ͮͯ ͯ͵ ͯͲ ͭͯ:ͯͱ Ͱͭ ͯʹ ͭͯ:ͯͱ Ͱͭ ͯʹ ͭͲ:ͭͱ Ͱͯ Ͱͬ ͭͲ:ͭͱ Ͱͱ Ͱͮ ͭͳ:ͯͲ ͯ͵ ͯͲ ͭͳ:ͯͲ ͯ͵ ͯͲ ͭ͵:ͱͯ ͯͯ ͯͭ ͭ͵:ͱͯ ͯͯ ͯͭ

Level ͮ. Intermediate Schedule BuildingChapter 3. Schedule Building 3-48 SOUTHBOUND Current Runtimes Proposed Runtimes Period Be- ginning Wishram Sand Point Period Beginning Wishram Sand Point Ͱ:ͭͬ ͯͯ ͯͮ Ͱ:ͭͬ ͯͯ ͯͮ ͱ:ͮͬ ͯͳ ͯͳ ͱ:ͮͬ ͯͳ ͯͳ Ͳ:ͱͬ Ͱͮ Ͱͭ Ͳ:ͱͬ Ͱͮ Ͱͭ ͵:ͮͮ ͯͳ ͯͲ ͵:ͮͮ ͯͳ ͯͲ ͭͯ:ͯͱ ͯ͵ ͯʹ ͭͯ:ͯͱ Ͱͬ ͯ͵ ͭͱ:ͯͯ Ͱͯ Ͱͮ ͭͲ:ͮͬ Ͱͮ Ͱͭ ͭͲ:ͮͬ ͰͲ Ͱͱ ͭͳ:ͯͬ Ͱͬ ͯ͵ ͭͳ:ͯͬ Ͱͮ Ͱͭ ͭʹ:ͱͬ ͯͲ ͯͱ ͭʹ:ͱͬ ͯͳ ͯͲ ͮͭ:ͬͱ ͯͭ ͯͬ ͮͭ:ͬͱ ͯͭ ͯͬ Clearly, the southbound direction running time gets the biggest adjustment. In the PM peak four minutes will be added to both branches over the present allowances. In contrast, only minor changes are made to the ͭͲ:ͭͱ peak running time period in the northbound direction. An additional running time period (from ͭͱ:ͯͯ to ͭͲ:ͮͬ) is added in the southbound direction, both in order to help ramp up running times smoothly and because added running time is needed that early in the PM. There is an additional running time after the PM peak when running times are dropping by as much as Ͳ minutes per period. Experience has shown that it is relatively easy to smooth out the running time transition, since the headway will be widening through- out that time as well. In the advanced section, you will take these changes and incorporate them into a fully revised Route ͵Ͳ schedule, with new running times that diff er throughout the day and adjusted head- ways to meet demand.

Chapter 3. Schedule Building 3-49 Level Í®. Intermediate Schedule Building LEVEL 2B End of Intermediate Schedule Building, Part B. The Advanced Section of Schedule Building continues on the next page. To jump to Schedule Blocking, go to page Í°-Í­.

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-50 LEVEL 3A 3.4 Advanced Schedule Building—Adjusting a More Complex Schedule Based on Check Data Schedulers are often in the position where minor changes need to be made to ex- isting schedules. The previous section showed how to analyze traffi c check data to fi nd instances where the present schedule is no longer functioning properly. In the case of Route ͵Ͳ, both the ridership and running time have increased beyond the ability of the schedule to properly do its job. The scope of change is clear from the preceding section: additional running time is needed in the PM peak and an additional trip is also needed to bring loads down within prescribed stan- dards. The change will require at least one additional bus, because the layover in the present schedule is as tight as possible. The fi rst step is to calculate the new round trip cycle with the additional running time to see what eff ect this will have on the bus count. The second step is to change the headway from ͭͬ to ʹ minutes in the peak of the PM peak. The longest round trip running time (using the longest branch, ͵Ͳ to Libby & Wishram as we did the fi rst time) is now ͰͲ + Ͱͯ = ʹ͵ minutes. We are presently scheduling a ͭͬ-minute inter- val/headway. If we were to continue to use nine buses, it would give us a ͵ͬ-minute cycle (͵ buses x ͭͬ-minute headway). So even without the addition of a trip to achieve eight minute service in the peak of the peak, the additional running time leaves insuffi cient layover on sev- eral trips. The example below tries unsuccessfully to fi t the new running times into the existing schedule. Several southbound trips (highlighted in gray) have either no layover or negative layover time, and layover time on northbound trips is too tight to adjust.

Chapter 3. Schedule Building 3-51 Level ͯ. Advanced Schedule Building Adding a tenth bus results in a ͭͬͬ-minute cycle (ͭͬ x ͭͬ), which is achievable for the existing ͭͬ-minute headway. The goal is to keep the southbound headway as even as possible. In the spreadsheet, the leaving times of all trips which will need their running time adjusted are high- lighted. Running time periods with revised times southbound begin at ͭͯ:ͯͬ and extend to just before ͮͭ:ͬͬ. New northbound running times are needed beginning at ͭͲ:ͭͱ and extending un- til ͭͳ:ͯͲ. Choose the leaving times of these trips and highlight them in gray, as shown below. S C H E D U L E S H E E T - R e vis e d runn ing tim e s in o rig ina l sc he d ule Route 96 IN EFF: S eptem ber 15, 2007 M O NDAY THRU FRIDAY NO RTHB O UND S O UTHB O UND OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN BLK GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 2 15:23 15:33 15:44 15:51 16:01 16:09 16:20 16:28 16:39 16:52 16:52 3 15:35 15:48 15:59 16:06 16:16 16:20 16:32 16:41 16:53 17:05 17:05 4 15:48 15:58 16:09 16:16 16:26 16:30 16:42 16:51 17:03 17:16 17:15 11 15:53 16:08 16:19 16:26 16:36 16:40 16:52 17:01 17:13 17:25 17:28 5 16:05 16:18 16:29 16:36 16:46 16:50 17:02 17:11 17:23 17:36 17:36 12 16:15 16:25 16:36 16:44 16:55 17:00 17:12 17:21 17:33 17:45 17:53 13 16:20 16:35 16:46 16:54 17:05 17:10 17:22 17:31 17:43 17:56 18:05 6 16:32 16:46 16:58 17:06 17:17 17:20 17:32 17:41 17:53 18:05 18:25 1 16:45 16:56 17:08 17:16 17:27 17:30 17:41 17:49 18:00 18:12 18:35 2 16:52 17:06 17:18 17:26 17:37 17:40 17:51 17:59 18:10 18:21 18:23 3 17:05 17:16 17:28 17:36 17:47 17:52 18:03 18:11 18:22 18:34 18:54 4 17:15 17:29 17:41 17:49 18:00 18:05 18:16 18:24 18:35 18:46 18:53 11 17:28 17:39 17:51 17:59 18:10 18:20

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-52 S C HE D UL E S HE E T with trip s ne e d ing ne w tim e s hig hlig hte d R o u te 96 IN EF F : S ep tem be r 15 , 200 7 M O NDA Y T HRU F R IDA Y N O R TH B O UN D S O U TH B O UN D OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 12 :53 13 :03 13 :13 13 :20 13 :29 13 :35 13 :45 13 :52 14 :03 14 :13 14 :23 13 :05 13 :18 13 :28 13 :35 13 :44 13 :50 14 :00 14 :07 14 :18 14 :29 14 :35 13 :23 13 :33 13 :43 13 :50 13 :59 14 :05 14 :15 14 :22 14 :33 14 :43 14 :53 13 :35 13 :48 13 :59 14 :06 14 :16 14 :20 14 :30 14 :37 14 :48 14 :59 15 :05 13 :53 14 :03 14 :14 14 :21 14 :31 14 :35 14 :45 14 :52 15 :03 15 :13 15 :23 14 :05 14 :18 14 :29 14 :36 14 :46 14 :50 15 :00 15 :07 15 :18 15 :29 15 :35 14 :23 14 :33 14 :44 14 :51 15 :01 15 :05 15 :15 15 :22 15 :33 15 :43 15 :48 14 :35 14 :48 14 :59 15 :06 15 :16 15 :20 15 :30 15 :37 15 :48 15 :59 16 :05 15 :23 15 :33 15 :43 15 :50 16 :01 16 :11 16 :15 14 :53 15 :03 15 :14 15 :21 15 :31 15 :45 15 :55 16 :02 16 :13 16 :24 16 :32 15 :05 15 :18 15 :29 15 :36 15 :46 15 :57 16 :07 16 :14 16 :25 16 :35 16 :45 15 :23 15 :33 15 :44 15 :51 16 :01 16 :09 16 :19 16 :26 16 :37 16 :48 16 :52 15 :35 15 :48 15 :59 16 :06 16 :16 16 :20 16 :31 16 :39 16 :50 17 :01 17 :05 15 :48 15 :58 16 :09 16 :16 16 :26 16 :30 16 :41 16 :49 17 :00 17 :12 17 :15 15 :53 16 :08 16 :19 16 :26 16 :36 16 :40 16 :51 16 :59 17 :10 17 :21 17 :28 16 :05 16 :18 16 :29 16 :36 16 :46 16 :50 17 :01 17 :09 17 :20 17 :32 17 :36 16 :15 16 :25 16 :36 16 :44 16 :55 17 :00 17 :11 17 :19 17 :30 17 :41 17 :53 16 :20 16 :35 16 :46 16 :54 17 :05 17 :10 17 :21 17 :29 17 :40 17 :52 18 :05 16 :32 16 :45 16 :56 17 :04 17 :15 17 :20 17 :31 17 :39 17 :50 18 :01 18 :21 16 :45 16 :55 17 :06 17 :14 17 :25 17 :30 17 :40 17 :48 17 :58 18 :10 18 :35 16 :52 17 :05 17 :16 17 :24 17 :35 17 :40 17 :50 17 :58 18 :08 18 :19 18 :23 17 :05 17 :15 17 :26 17 :34 17 :45 17 :52 18 :02 18 :10 18 :20 18 :32 18 :52 17 :15 17 :28 17 :39 17 :47 17 :58 18 :05 18 :15 18 :23 18 :33 18 :44 18 :53 17 :28 17 :38 17 :49 17 :57 18 :08 18 :18 17 :36 17 :49 17 :59 18 :06 18 :15 18 :20 18 :30 18 :38 18 :48 19 :00 19 :05 17 :53 18 :03 18 :13 18 :20 18 :29 18 :35 18 :45 18 :53 19 :03 19 :14 19 :23 18 :05 18 :18 18 :28 18 :35 18 :44 18 :50 18 :59 19 :06 19 :15 19 :26 19 :35 18 :23 18 :33 18 :43 18 :50 18 :59 19 :05 19 :14 19 :21 19 :30 19 :40 19 :53 18 :35 18 :48 18 :58 19 :05 19 :14 19 :25 19 :34 19 :41 19 :50 20 :01 20 :06 18 :53 19 :03 19 :13 19 :20 19 :29 19 :45 19 :54 20 :01 20 :10 20 :20 20 :28 19 :05 19 :18 19 :28 19 :35 19 :44 19 :54 19 :23 19 :33 19 :43 19 :50 19 :59 20 :05 20 :14 20 :21 20 :30 20 :41 20 :46 19 :35 19 :48 19 :58 20 :05 20 :14 20 :25 20 :34 20 :41 20 :50 21 :00 21 :08 19 :53 20 :03 20 :12 20 :19 20 :26 20 :36 20 :06 20 :18 20 :26 20 :32 20 :39 20 :45 20 :54 21 :01 21 :10 21 :21 21 :26

Chapter 3. Schedule Building 3-53 Level ͯ. Advanced Schedule Building Next, apply the new running times for these trips. Once the southbound trips are adjusted, do the same thing for the northbound direction. Northbound there is only one period that has changed, the ͭͲ:ͭͱ period, which encompasses trips leaving the two outer terminals after the ͭͲ:ͬͱ trip (at Libby) up to the ͭͳ:ͮʹ trip leaving Sand Point. The revised schedule refl ecting new running times is shown below. Blocks are not shown; the advanced section of the Block- ing chapter will show how to reblock this schedule. The spreadsheet shows that there are now four pull-outs in the PM peak, compared to three on the previous schedule: this is the tenth bus required. Some layovers are tight, especially the ͭͳ:ͱͬ arrival at Rugby Circle, but this bus will pull in after its next southbound trip. S C HE D UL E S HE E T with ne w running tim e s Ro u te 96 IN EF F : M O NDAY T HRU F RIDAY NO RTHB O UND S O UTHB O UND OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 12:53 13:03 13:13 13:20 13:29 13:35 13:45 13:52 14:03 14:14 14:23 13:05 13:18 13:28 13:35 13:44 13:50 14:00 14:07 14:18 14:30 14:35 13:23 13:33 13:43 13:50 13:59 14:05 14:15 14:22 14:33 14:44 14:53 13:35 13:48 13:59 14:06 14:16 14:20 14:30 14:37 14:48 15:00 15:05 13:53 14:03 14:14 14:21 14:31 14:35 14:45 14:52 15:03 15:14 15:23 14:05 14:18 14:29 14:36 14:46 14:50 15:00 15:07 15:18 15:30 15:35 14:23 14:33 14:44 14:51 15:01 15:05 15:15 15:22 15:33 15:44 15:48 14:35 14:48 14:59 15:06 15:16 15:20 15:30 15:37 15:48 16:00 16:05 15:23 15:33 15:44 15:52 16:03 16:15 16:23 14:53 15:03 15:14 15:21 15:31 15:45 15:56 16:04 16:15 16:28 16:30 15:05 15:18 15:29 15:36 15:46 15:57 16:08 16:16 16:27 16:39 16:43 15:23 15:33 15:44 15:51 16:01 16:09 16:20 16:28 16:39 16:52 17:13 15:35 15:48 15:59 16:06 16:16 16:20 16:32 16:41 16:53 17:05 17:08 15:48 15:58 16:09 16:16 16:26 16:30 16:42 16:51 17:03 17:16 17:35 15:53 16:08 16:19 16:26 16:36 16:40 16:52 17:01 17:13 17:25 17:28 16:05 16:18 16:29 16:36 16:46 16:50 17:02 17:11 17:23 17:36 17:56 16:13 16:28 16:39 16:46 16:56 17:00 17:12 17:21 17:33 17:45 17:53 16:23 16:34 16:46 16:54 17:05 17:10 17:22 17:31 17:43 17:56 18:05 16:30 16:44 16:56 17:04 17:15 17:20 17:32 17:41 17:53 18:05 18:23 16:43 16:54 17:06 17:14 17:25 17:30 17:41 17:49 18:00 18:12 18:35 16:20 16:50 17:04 17:16 17:24 17:35 17:40 17:51 17:59 18:10 18:21 18:41 17:08 17:19 17:31 17:39 17:50 17:52 18:03 18:11 18:22 18:34 18:54 17:13 17:27 17:39 17:47 17:58 18:05 18:16 18:24 18:35 18:46 18:53 17:28 17:39 17:51 17:59 18:10 18:20 17:35 17:48 17:59 18:06 18:15 18:20 18:31 18:39 18:50 19:02 19:05

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-54 Now that running times have been adjusted, the next step is to reduce peak headways. Adding an additional trip would again bring layover below acceptable levels. Thus, the expectation is that an eleventh bus will be needed to supply the additional southbound trip. First, add the new PM southbound trips originally sketched into the schedule. It then becomes obvious that the northbound trips will also have to be adjusted to make the new schedule work and all the trips in the PM peak and after will have to be reblocked. Portions of the schedule with headway adjustments are highlighted in dark gray, while added southbound trips are highlighted in light gray. S C HE D UL E S HE E T with ne w runn ing tim e s and re vis e d s o uthb o und he ad ways R ou te 96 IN EFF : M O NDA Y T HRU F R IDA Y N O R TH B O UN D S O U TH B O UN D OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 12 :53 13 :03 13 :13 13 :20 13 :29 13 :35 13 :45 13 :52 14 :03 14 :14 14 :23 13 :05 13 :18 13 :28 13 :35 13 :44 13 :50 14 :00 14 :07 14 :18 14 :30 14 :35 13 :23 13 :33 13 :43 13 :50 13 :59 14 :05 14 :15 14 :22 14 :33 14 :44 14 :53 13 :35 13 :48 13 :59 14 :06 14 :16 14 :20 14 :30 14 :37 14 :48 15 :00 15 :05 13 :53 14 :03 14 :14 14 :21 14 :31 14 :35 14 :45 14 :52 15 :03 15 :14 15 :23 14 :05 14 :18 14 :29 14 :36 14 :46 14 :50 15 :00 15 :07 15 :18 15 :30 15 :35 14 :23 14 :33 14 :44 14 :51 15 :01 15 :05 15 :15 15 :22 15 :33 15 :44 15 :48 14 :35 14 :48 14 :59 15 :06 15 :16 15 :20 15 :30 15 :37 15 :48 16 :00 16 :05 15 :23 15 :33 15 :44 15 :52 16 :03 16 :15 16 :23 14 :53 15 :03 15 :14 15 :21 15 :31 15 :45 15 :56 16 :04 16 :15 16 :28 16 :30 15 :05 15 :18 15 :29 15 :36 15 :46 15 :57 16 :08 16 :16 16 :27 16 :39 16 :43 15 :23 15 :33 15 :44 15 :51 16 :01 16 :09 16 :20 16 :28 16 :39 16 :52 16 :55 15 :35 15 :48 15 :59 16 :06 16 :16 16 :20 16 :32 16 :41 16 :53 17 :05 17 :08 15 :48 15 :58 16 :09 16 :16 16 :26 16 :29 16 :41 16 :50 17 :02 17 :15 17 :17 15 :53 16 :08 16 :19 16 :26 16 :36 16 :37 16 :49 16 :58 17 :10 17 :22 17 :28 16 :05 16 :18 16 :29 16 :36 16 :46 16 :45 16 :57 17 :06 17 :18 17 :31 16 :13 16 :28 16 :39 16 :46 16 :56 16 :53 17 :05 17 :14 17 :26 17 :39 17 :59 16 :23 16 :34 16 :46 16 :54 17 :05 17 :01 17 :13 17 :22 17 :34 17 :46 17 :53 16 :30 16 :44 16 :56 17 :04 17 :15 17 :09 17 :21 17 :30 17 :42 17 :55 18 :05 16 :43 16 :54 17 :06 17 :14 17 :25 17 :17 17 :29 17 :38 17 :50 18 :02 18 :23 16 :20 16 :50 17 :04 17 :16 17 :24 17 :35 17 :25 17 :37 17 :46 17 :58 18 :10 17 :08 17 :19 17 :31 17 :39 17 :50 17 :35 17 :46 17 :54 18 :05 18 :17 18 :35 17 :13 17 :27 17 :39 17 :47 17 :58 17 :45 17 :56 18 :04 18 :15 18 :26 18 :46 17 :28 17 :39 17 :51 17 :59 18 :10 17 :55 18 :06 18 :14 18 :25 18 :37 18 :57 17 :35 17 :48 17 :59 18 :06 18 :15 18 :20 17 :53 18 :03 18 :13 18 :20 18 :29 18 :07 18 :18 18 :26 18 :37 18 :48 18 :53 18 :05 18 :18 18 :28 18 :35 18 :44 18 :20 18 :31 18 :39 18 :50 19 :02 19 :05

Chapter 3. Schedule Building 3-55 Level ͯ. Advanced Schedule Building One goal in adding trips was to keep the times at the MLP (Pasco & Havre) to those identifi ed earlier, while working toward an “evenness” in the trip leaving times from Rugby Circle. Even- ness means a normal progression of headway narrowing and then widening as times approach the trips that are not being changed. A comparison of current and proposed trip leaving times for the period of change is shown below. Lvg. Rugby Cir. 16:09 16:09 16:20 16:20 16:30 16:29 16:40 16:37 16:45 16:50 16:53 17:00 17:01 17:10 17:09 17:20 17:17 17:25 17:30 17:35 17:40 17:45 17:52 17:55 18:05 18:07 18:20 18:20 The headway progression is smooth and puts the additional trip where it is needed. Note that two trips have actually been added in order to carry the headway back to the original schedule at ͭʹ:ͮͬ. This has an advantage later on in reblocking the schedule. If only one trip is added to a two-branch route, the trips throughout the remainder of the day would be reversed to each branch. Now the running time has been adjusted in both directions, and new southbound trips have been added. Study your progress so far. In two cases, two consecutive trips serve the same outer terminal (the ͭͲ:Ͱͱ and ͭͲ:ͱͯ trips and the ͭͳ:ͭͳ and ͭͳ:ͮͱ trips). The solution is to “fl ip” the terminals until we reach the second added trip, after which the trips again fall to their pre- vious end points. This is shown below, with fl ipped trips highlighted in dark gray. When adding rows or columns to a schedule in a spreadsheet, add only the cells needed and shift the other cells down. Adding whole rows can disturb other information on the spreadsheet, such as the running time table area. Tip

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-56 S C HE D UL E S HE E T with ne w runn ing tim e s and "f lip p e d " s o uthb o und trip s R o u te 9 6 IN EF F : M O N D A Y T H R U F R ID A Y N O R TH B O U N D S O U TH B O U N D OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 12 :5 3 13 :0 3 13 :1 3 13 :2 0 13 :2 9 13 :3 5 13 :4 5 13 :5 2 14 :0 3 14 :1 4 14 :2 3 13 :0 5 13 :1 8 13 :2 8 13 :3 5 13 :4 4 13 :5 0 14 :0 0 14 :0 7 14 :1 8 14 :3 0 14 :3 5 13 :2 3 13 :3 3 13 :4 3 13 :5 0 13 :5 9 14 :0 5 14 :1 5 14 :2 2 14 :3 3 14 :4 4 14 :5 3 13 :3 5 13 :4 8 13 :5 9 14 :0 6 14 :1 6 14 :2 0 14 :3 0 14 :3 7 14 :4 8 15 :0 0 15 :0 5 13 :5 3 14 :0 3 14 :1 4 14 :2 1 14 :3 1 14 :3 5 14 :4 5 14 :5 2 15 :0 3 15 :1 4 15 :2 3 14 :0 5 14 :1 8 14 :2 9 14 :3 6 14 :4 6 14 :5 0 15 :0 0 15 :0 7 15 :1 8 15 :3 0 15 :3 5 14 :2 3 14 :3 3 14 :4 4 14 :5 1 15 :0 1 15 :0 5 15 :1 5 15 :2 2 15 :3 3 15 :4 4 15 :4 8 14 :3 5 14 :4 8 14 :5 9 15 :0 6 15 :1 6 15 :2 0 15 :3 0 15 :3 7 15 :4 8 16 :0 0 16 :0 5 15 :2 3 15 :3 3 15 :4 4 15 :5 2 16 :0 3 16 :1 5 16 :2 3 14 :5 3 15 :0 3 15 :1 4 15 :2 1 15 :3 1 15 :4 5 15 :5 6 16 :0 4 16 :1 5 16 :2 8 16 :3 0 15 :0 5 15 :1 8 15 :2 9 15 :3 6 15 :4 6 15 :5 7 16 :0 8 16 :1 6 16 :2 7 16 :3 9 16 :4 3 15 :2 3 15 :3 3 15 :4 4 15 :5 1 16 :0 1 16 :0 9 16 :2 0 16 :2 8 16 :3 9 16 :5 2 16 :5 5 15 :3 5 15 :4 8 15 :5 9 16 :0 6 16 :1 6 16 :2 0 16 :3 2 16 :4 1 16 :5 3 17 :0 5 17 :0 8 15 :4 8 15 :5 8 16 :0 9 16 :1 6 16 :2 6 16 :2 9 16 :4 1 16 :5 0 17 :0 2 17 :1 5 17 :1 7 15 :5 3 16 :0 8 16 :1 9 16 :2 6 16 :3 6 16 :3 7 16 :4 9 16 :5 8 17 :1 0 17 :2 2 17 :2 8 16 :0 5 16 :1 8 16 :2 9 16 :3 6 16 :4 6 16 :4 5 16 :5 7 17 :0 6 17 :1 8 17 :3 1 16 :1 3 16 :2 8 16 :3 9 16 :4 6 16 :5 6 16 :5 3 17 :0 5 17 :1 4 17 :2 6 17 :3 8 17 :5 9 16 :2 3 16 :3 4 16 :4 6 16 :5 4 17 :0 5 17 :0 1 17 :1 3 17 :2 2 17 :3 4 17 :4 7 17 :5 3 16 :3 0 16 :4 4 16 :5 6 17 :0 4 17 :1 5 17 :0 9 17 :2 1 17 :3 0 17 :4 2 17 :5 4 18 :0 5 16 :4 3 16 :5 4 17 :0 6 17 :1 4 17 :2 5 17 :1 7 17 :2 9 17 :3 8 17 :5 0 18 :0 3 18 :2 3 16 :2 0 16 :5 0 17 :0 4 17 :1 6 17 :2 4 17 :3 5 17 :2 5 17 :3 7 17 :4 6 17 :5 8 18 :1 0 17 :0 8 17 :1 9 17 :3 1 17 :3 9 17 :5 0 17 :3 5 17 :4 6 17 :5 4 18 :0 5 18 :1 7 18 :3 5 17 :1 3 17 :2 7 17 :3 9 17 :4 7 17 :5 8 17 :4 5 17 :5 6 18 :0 4 18 :1 5 18 :2 6 18 :4 6 17 :2 8 17 :3 9 17 :5 1 17 :5 9 18 :1 0 17 :5 5 18 :0 6 18 :1 4 18 :2 5 18 :3 7 18 :5 7 17 :3 5 17 :4 8 17 :5 9 18 :0 6 18 :1 5 18 :2 0 17 :5 3 18 :0 3 18 :1 3 18 :2 0 18 :2 9 18 :0 7 18 :1 8 18 :2 6 18 :3 7 18 :4 8 18 :5 3 18 :0 5 18 :1 8 18 :2 8 18 :3 5 18 :4 4 18 :2 0 18 :3 1 18 :3 9 18 :5 0 19 :0 2 19 :0 5

Chapter 3. Schedule Building 3-57 Level ͯ. Advanced Schedule Building When adding trips on a route with branches, avoid unintended effects in other time periods. Night service to each branch might be timed to meet the closing time at a shopping center, or riders might simply have learned to depend on specifi c trip times when headways are at their widest. The ideal solution when working on a two-branch route is to add two trips. Tip The fi nal step in our schedule adjustment is to add in northbound trips corresponding to the southbound trips already added. Results are shown below, with changed trips highlighted in gray. There are now fi ve PM pullouts, refl ecting the addition of the eleventh bus. SC HED ULE SHE ET with ad jus te d running tim e and headways R o u te 96 IN EF F : M O NDA Y T HRU F R IDA Y N O R TH B O UN D S O U TH B O UN D OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 12 :53 13 :03 13 :13 13 :20 13 :29 13 :35 13 :45 13 :52 14 :03 14 :14 14 :23 13 :05 13 :18 13 :28 13 :35 13 :44 13 :50 14 :00 14 :07 14 :18 14 :30 14 :35 13 :23 13 :33 13 :43 13 :50 13 :59 14 :05 14 :15 14 :22 14 :33 14 :44 14 :53 13 :35 13 :48 13 :59 14 :06 14 :16 14 :20 14 :30 14 :37 14 :48 15 :00 15 :05 13 :53 14 :03 14 :14 14 :21 14 :31 14 :35 14 :45 14 :52 15 :03 15 :14 15 :23 14 :05 14 :18 14 :29 14 :36 14 :46 14 :50 15 :00 15 :07 15 :18 15 :30 15 :35 14 :23 14 :33 14 :44 14 :51 15 :01 15 :05 15 :15 15 :22 15 :33 15 :44 15 :48 14 :35 14 :48 14 :59 15 :06 15 :16 15 :20 15 :30 15 :37 15 :48 16 :00 16 :05 15 :23 15 :33 15 :44 15 :52 16 :03 16 :15 16 :23 14 :53 15 :03 15 :14 15 :21 15 :31 15 :45 15 :56 16 :04 16 :15 16 :28 16 :30 15 :05 15 :18 15 :29 15 :36 15 :46 15 :57 16 :08 16 :16 16 :27 16 :39 16 :41 15 :23 15 :33 15 :44 15 :51 16 :01 16 :09 16 :20 16 :28 16 :39 16 :52 16 :55 15 :35 15 :48 15 :59 16 :06 16 :16 16 :20 16 :32 16 :41 16 :53 17 :05 17 :08 16 :19 16 :29 16 :41 16 :50 17 :02 17 :15 17 :17 15 :48 15 :58 16 :09 16 :16 16 :26 16 :37 16 :49 16 :58 17 :10 17 :22 17 :28 15 :53 16 :08 16 :19 16 :26 16 :36 16 :45 16 :57 17 :06 17 :18 17 :31 17 :40 16 :05 16 :18 16 :29 16 :36 16 :46 16 :53 17 :05 17 :14 17 :26 17 :38 17 :53 16 :11 16 :26 16 :38 16 :46 16 :57 17 :01 17 :13 17 :22 17 :34 17 :47 18 :07 16 :23 16 :34 16 :46 16 :54 17 :05 17 :09 17 :21 17 :30 17 :42 17 :54 18 :14 16 :30 16 :44 16 :56 17 :04 17 :15 17 :17 17 :29 17 :38 17 :50 18 :03 18 :05 16 :41 16 :52 17 :04 17 :12 17 :23 17 :25 17 :37 17 :46 17 :58 18 :10 18 :23 16 :45 17 :00 17 :12 17 :20 17 :31 17 :35 17 :46 17 :54 18 :05 18 :17 18 :35 16 :55 17 :09 17 :21 17 :29 17 :40 17 :45 17 :56 18 :04 18 :15 18 :26 18 :46 17 :08 17 :19 17 :31 17 :39 17 :50 17 :55 18 :06 18 :14 18 :25 18 :37 18 :57 17 :17 17 :31 17 :43 17 :51 18 :02 18 :07 18 :18 18 :26 18 :37 18 :48 18 :53 17 :28 17 :39 17 :51 17 :59 18 :10 18 :20 18 :31 18 :39 18 :50 19 :02 19 :05 17 :40 17 :53 18 :03 18 :10 18 :19 18 :29

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-58 This schedule provides an eight-minute headway for about Ͱͬ minutes in the peak of the peak period. Note that with an eleventh bus, the cycle calculates to ʹʹ minutes (ʹ x ͭͭ buses). But our adjusted round trip running time is ʹ͵ minutes! The reason that this schedule works is that the eight-minute headway is in place for only about half the peak round trip cycle. Some buses will not be making a full cycle during the time when the headways are tightest and running time longest and therefore will not require the full ʹ͵ minutes allocated to a round-trip. It is always smart to draft a revised schedule and not to rely solely on the cycle calculation. There are some tight layover situations at both ends of the route. Usually, no bus faces tight layover twice, with the exception of the southbound trip leaving Rugby Circle at ͭͱ:ͱͳ. It gets just two minutes at Sand Point and then only two minutes on arrival at Rugby Circle at ͭͳ:ͮͯ. In most other cases, a minimum layover is followed by a more generous layover time at the other end. Some systems’ layover rules might not allow this, but on many properties, minimum layover is specifi cally allowed during peak times. Note also that the northbound headways are not uniform. The ͭͳ:ͭͳ trip departing Wishram provides a ͭͮ-minute headway further up the line in a period where other buses are running ͭͬ minutes apart. This two-minute delay to the departure was done in order to allow enough layover for the trip arriving Wishram at ͭͳ:ͭͱ to be able to hook to it. The trip adjustments also show up in less than ideal leaving times from the outer terminals, particularly Sand Point. Leaving times would be more uniform if the ͭͲ:ͮͯ Sand Point depar- ture could be moved to the next earlier trip, which would have it leave at ͭͲ:ͭͱ. This earlier trip is a pull-out at ͭͲ:ͭͭ, which fi ts into the route at Pasco & Essex, just as other pull-outs to that point have been scheduled. To make the earlier trip the Sand Point trip presents logisti- cal problems, specifi cally what to do with the bus that arrives at Sand Point at ͭͲ:ͭͱ. Sending the bus out with zero layover is not an option. And if the ͭͲ:ͭͱ departure is scheduled using the pull-out, another Sand Point departure would be needed to have something for the ͭͲ:ͭͱ arrival to hook up with. The ͭͲ:ͮͯ departure could be left alone, but this trip would be a waste, scheduled just eight minutes after the previous departure. In addition, the scheduled pull-out at ͭͲ:ͭͭ would have to leave from the garage at about ͭͱ:ͱͱ, adding another ͭͲ minutes to the platform time of the schedule. A good scheduler always weighs these adjustments to see which one would provide the greatest service at the least cost. In this case, the swapping of trips is considered unnecessary in view of what would be gained, and the northbound schedule is not changed. Undoubtedly there are other minor ways the northbound trip grid could have been adjusted to achieve a similar result, but the one shown does the job. It provides suffi cient running time, a The addition of peak buses is not a trivial matter at any system. Because of budget constraints, on most sys- tems, the addition of a peak bus on one route might require that the bus be taken from another route, so that the overall system does not have a net increase. In many cases, transit systems experience unbalanced peaks, requiring more buses in one peak than the other. If our sample system has its highest bus count in the AM peak, then adding a PM peak bus is not as diffi cult, even though there will be a cost conse- quence for the additional hours. The true scheduling practitioner simply does not part with another bus unless all other alternatives have been exhausted. Tip

Chapter 3. Schedule Building 3-59 Level ͯ. Advanced Schedule Building reasonably even headway and distribution of trips from the end terminals, and two new south- bound trips, all for the two additional buses. Now that the trips are in place, the next steps are to make sure that every trip hooks properly and then begin the process of reblocking, starting at the beginning of the PM pull-outs. These steps will be addressed in the advanced section of Chapter Ͱ. A sneak preview: there is enough of a change that no block fi nishes its day the same as it did in the original schedule. The chang- es will add two peak buses, as we noted here, and about four platform hours. The fi nal sched- ule is shown below. S C HE D UL E S HE E T with ad jus te d running tim e and he ad ways Ro u te 96 IN EF F : M O NDAY T HRU F RIDAY P art 1 NO RTHB O UND S O UTHB O UND OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN BLK GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 5 4:10 4:20 4:28 4:35 4:43 4:53 5:05 1 3:45 4:05 4:18 4:26 4:33 4:41 4:50 4:58 5:05 5:13 5:23 5:35 6 4:55 5:05 5:13 5:20 5:28 5:37 5:49 3 4:05 4:35 4:48 4:56 5:03 5:11 5:20 5:29 5:37 5:47 5:57 6:05 7 4:39 4:59 5:08 5:16 5:23 5:31 5:35 5:44 5:52 6:02 6:12 6:19 5 5:05 5:19 5:29 5:37 5:46 5:50 5:59 6:07 6:17 6:27 6:45 9 4:59 5:19 5:29 5:39 5:47 5:56 6:05 6:14 6:22 6:32 6:42 6:57 1 5:35 5:49 5:59 6:07 6:16 6:20 6:29 6:37 6:47 6:57 7:05 6 5:49 5:59 6:09 6:17 6:26 6:35 6:44 6:52 7:02 7:12 7:17 3 6:05 6:19 6:29 6:37 6:46 6:50 7:01 7:10 7:21 7:32 7:45 7 6:19 6:29 6:39 6:47 6:56 7:05 7:16 7:25 7:36 7:46 7:57 8 5:55 6:25 6:39 6:50 6:59 7:10 7:15 7:26 7:35 7:46 7:57 8:05 4 6:17 6:37 6:49 7:00 7:09 7:20 7:25 7:36 7:45 7:56 8:06 8:23 5 6:45 6:59 7:10 7:19 7:30 7:35 7:46 7:55 8:06 8:17 8:35 9 6:57 7:09 7:20 7:29 7:40 7:45 7:56 8:05 8:16 8:26 8:46 1 7:05 7:19 7:30 7:39 7:50 7:55 8:06 8:15 8:26 8:37 9:05 6 7:17 7:29 7:40 7:49 8:00 8:05 8:16 8:25 8:36 8:46 8:53 10 6:55 7:25 7:39 7:50 7:59 8:10 8:15 8:26 8:35 8:46 8:57 9:17 2 7:17 7:37 7:49 8:00 8:09 8:20 8:25 8:36 8:45 8:56 9:06 9:23 3 7:45 7:59 8:10 8:19 8:30 8:35 8:46 8:55 9:06 9:17 9:35 7 7:57 8:09 8:20 8:29 8:40 8:45 8:56 9:05 9:16 9:26 9:46 8 8:05 8:19 8:30 8:39 8:50 8:55 9:06 9:15 9:26 9:37 9:57 4 8:23 8:34 8:44 8:52 9:02 9:07 9:18 9:27 9:38 9:48 9:53 5 8:35 8:48 8:58 9:06 9:16 9:22 9:32 9:40 9:50 10:01 10:05 6 8:53 9:04 9:14 9:21 9:31 9:37 9:46 9:53 10:03 10:13 10:23 1 9:05 9:18 9:28 9:35 9:44 9:52 10:01 10:08 10:18 10:29 10:35 2 9:23 9:33 9:43 9:50 9:59 10:07 10:16 10:23 10:33 10:43 10:53 3 9:35 9:48 9:58 10:05 10:14 10:22 10:31 10:38 10:48 10:59 11:05 4 9:53 10:03 10:13 10:20 10:29 10:37 10:46 10:53 11:03 11:13 11:23 5 10:05 10:18 10:28 10:35 10:44 10:52 11:01 11:08 11:18 11:29 11:35 6 10:23 10:33 10:43 10:50 10:59 11:07 11:16 11:23 11:33 11:43 11:53 1 10:35 10:48 10:58 11:05 11:14 11:22 11:31 11:38 11:48 11:59 12:05 2 10:53 11:03 11:13 11:20 11:29 11:37 11:46 11:53 12:03 12:13 12:23 3 11:05 11:18 11:28 11:35 11:44 11:52 12:01 12:08 12:18 12:29 12:35 4 11:23 11:33 11:43 11:50 11:59 12:07 12:16 12:23 12:33 12:43 12:53 5 11:35 11:48 11:58 12:05 12:14 12:22 12:31 12:38 12:48 12:59 13:05 6 11:53 12:03 12:13 12:20 12:29 12:37 12:46 12:53 13:03 13:13 13:23 1 12:05 12:18 12:28 12:35 12:44 12:52 13:01 13:08 13:18 13:29 13:35 2 12:23 12:33 12:43 12:50 12:59 13:07 13:16 13:23 13:33 13:43 13:53 3 12:35 12:48 12:58 13:05 13:14 13:22 13:31 13:38 13:48 13:59 14:05 4 12:53 13:03 13:13 13:20 13:29 13:35 13:45 13:52 14:03 14:14 14:23 5 13:05 13:18 13:28 13:35 13:44 13:50 14:00 14:07 14:18 14:30 14:35 6 13:23 13:33 13:43 13:50 13:59 14:05 14:15 14:22 14:33 14:44 14:53 1 13:35 13:48 13:59 14:06 14:16 14:20 14:30 14:37 14:48 15:00 15:05

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-60 S C HE D UL E S HE E T with ad jus te d running tim e and he ad ways Ro u te 96 IN EF F : M O NDAY T HRU F RIDAY P art 2 NO RTHB O UND S O UTHB O UND OUT Libby Sand Pasco Pasco Pasco Rugby Rugby Pasco Pasco Pasco Sand Libby IN BLK GAR Wishrm Point Essex Havre Willis Circle Circle Willis Havre Essex Point Wishrm GAR LVE. 2 13:53 14:03 14:14 14:21 14:31 14:35 14:45 14:52 15:03 15:14 15:23 3 14:05 14:18 14:29 14:36 14:46 14:50 15:00 15:07 15:18 15:30 15:35 4 14:23 14:33 14:44 14:51 15:01 15:05 15:15 15:22 15:33 15:44 15:48 5 14:35 14:48 14:59 15:06 15:16 15:20 15:30 15:37 15:48 16:00 16:05 15 15:23 15:33 15:44 15:52 16:03 16:15 16:23 6 14:53 15:03 15:14 15:21 15:31 15:45 15:56 16:04 16:15 16:28 16:30 1 15:05 15:18 15:29 15:36 15:46 15:57 16:08 16:16 16:27 16:39 16:41 2 15:23 15:33 15:44 15:51 16:01 16:09 16:20 16:28 16:39 16:52 16:55 3 15:35 15:48 15:59 16:06 16:16 16:20 16:32 16:41 16:53 17:05 17:08 12 16:19 16:29 16:41 16:50 17:02 17:15 17:17 4 15:48 15:58 16:09 16:16 16:26 16:37 16:49 16:58 17:10 17:22 17:28 13 15:53 16:08 16:19 16:26 16:36 16:45 16:57 17:06 17:18 17:31 17:40 5 16:05 16:18 16:29 16:36 16:46 16:53 17:05 17:14 17:26 17:38 17:53 14 16:11 16:26 16:38 16:46 16:57 17:01 17:13 17:22 17:34 17:47 18:07 15 16:23 16:34 16:46 16:54 17:05 17:09 17:21 17:30 17:42 17:54 18:14 6 16:30 16:44 16:56 17:04 17:15 17:17 17:29 17:38 17:50 18:03 18:05 1 16:41 16:52 17:04 17:12 17:23 17:25 17:37 17:46 17:58 18:10 18:23 11 16:45 17:00 17:12 17:20 17:31 17:35 17:46 17:54 18:05 18:17 18:35 2 16:55 17:09 17:21 17:29 17:40 17:45 17:56 18:04 18:15 18:26 18:46 3 17:08 17:19 17:31 17:39 17:50 17:55 18:06 18:14 18:25 18:37 18:57 12 17:17 17:31 17:43 17:51 18:02 18:07 18:18 18:26 18:37 18:48 18:53 4 17:28 17:39 17:51 17:59 18:10 18:20 18:31 18:39 18:50 19:02 19:05 13 17:40 17:53 18:03 18:10 18:19 18:29 5 17:53 18:03 18:13 18:20 18:29 18:35 18:46 18:54 19:05 19:16 19:23 6 18:05 18:18 18:28 18:35 18:44 18:50 18:59 19:06 19:16 19:27 19:35 1 18:23 18:33 18:43 18:50 18:59 19:05 19:14 19:21 19:31 19:41 19:53 11 18:35 18:48 18:58 19:05 19:14 19:25 19:34 19:41 19:51 20:02 20:06 12 18:53 19:03 19:13 19:20 19:29 19:45 19:54 20:01 20:11 20:21 20:28 4 19:05 19:18 19:28 19:35 19:44 19:54 5 19:23 19:33 19:43 19:50 19:59 20:05 20:14 20:21 20:31 20:42 20:46 6 19:35 19:48 19:58 20:05 20:14 20:25 20:34 20:41 20:51 21:01 21:08 1 19:53 20:03 20:12 20:19 20:26 20:36 11 20:06 20:18 20:26 20:32 20:39 20:45 20:54 21:01 21:11 21:22 21:26 12 20:28 20:38 20:46 20:52 20:59 21:05 21:14 21:21 21:31 21:41 21:48 5 20:46 20:58 21:06 21:12 21:19 21:25 21:34 21:41 21:51 22:02 22:06 6 21:08 21:18 21:26 21:32 21:39 21:45 21:54 22:01 22:11 22:21 22:28 11 21:26 21:38 21:46 21:52 21:59 22:05 22:14 22:21 22:31 22:42 22:46 12 21:48 21:58 22:06 22:12 22:19 22:25 22:34 22:41 22:51 23:01 23:08 5 22:06 22:18 22:26 22:32 22:39 22:45 22:54 23:01 23:11 23:22 23:26 6 22:28 22:38 22:46 22:52 22:59 23:05 23:14 23:21 23:31 23:41 23:48 11 22:46 22:58 23:06 23:12 23:19 23:25 23:34 23:41 23:51 0:02 0:06 12 23:08 23:18 23:26 23:32 23:39 23:49 5 23:26 23:38 23:46 23:52 23:59 0:05 0:14 0:21 0:31 0:42 1:02 6 23:48 23:58 0:06 0:12 0:19 0:29 11 0:06 0:18 0:26 0:32 0:39 0:49

Chapter 3. Schedule Building 3-61 Level ͯ. Advanced Schedule Building To summarize this section: we took the information from the traffi c checks and made a real world example schedule change that incorporated both increased running time and the need for an additional trip. We did it in the least intrusive way, disturbing the riding habits of the patrons of this route to the least extent possible. Our “good scheduler” mentality is partially satisfi ed with this while the other part wants to go back and see if this adjustment can be done with the addition of only one bus. But remember that preliminary analysis showed the round trip cycle would have been impossibly tight—even more so than in the fi nal schedule.

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-62 LEVEL 3A End of Advanced Schedule Building, Part A Advanced Schedule Building, Part B continues on the next page. To jump to Schedule Blocking, go to page Ͱ-ͭ.

Chapter 3. Schedule Building 3-63 Level ͯ. Advanced Schedule Building 3.5 Advanced Topics In Schedule Writing LEVEL 3B Establishing Running Times Setting running times is a topic that generates much discussion and at times controversy within the transit industry. A quick review of available literature will indicate numerous research papers have been written addressing this topic. In addition a number of transit systems have undertaken studies of their own as to how best ap- proach running times methodology. The survey of transit operators, conducted as part of this project, revealed that taking averages of running time observations continues to be the most common way of setting running times on a route or route segment. Almost ʹͬ% of respondents use running time averages, often leavened with professional judgment. In systems without APCs or AVL, the scheduler will typi- cally eliminate any unusual values from the running time observations at hand and average the remaining data. Use of APC and AVL yield many more observations to be included in averages. Does greater availability of running time data allow for new ways to establish running times in a schedule? It might provide some perspective for this discussion to consider the scheduler’s goals in set- ting running times on a route: ͭ. To provide an accurate and reliable timetable for customers to use. The scheduler wants to set times at each time point with a high probability that the actual arrival or departure time will match the scheduled time. Reliability is an important element of service quality as perceived by the customer. ͮ. To provide a realistic schedule for operators so that they can drive at a reasonable, safe speed. ͯ. To ensure an effi cient operation. The scheduler has a direct impact on operational costs and, by minimizing unproductive time, can enhance effi ciency. Ͱ. To avoid instances of running hot, a major transgression in transit operations. ͱ. To eliminate or sharply reduce situations where running time is too tight and service runs late or is subject to buses bunching. Ͳ. To maximize on-time performance. As discussed in the intermediate section of this chapter, each agency has a specifi c defi nition of “on time.” Typically, a trip is considered on time if it arrives or departs from a time point within ͬ to ͱ minutes after the sched- uled arrival/departure time. Customer information systems may estimate scheduled time at intermediate stops, increasing pressure not to run early prior to a time point.

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-64 The impact of running times can be a signifi cant factor in unreliable operations, particularly with regard to bunching of vehicles. While bunching is often caused by varying operating con- ditions (traffi c, congestion, loading variability, etc.) the scheduled run times can aff ect whether vehicles operate early or late. And once vehicles fall outside the schedule, this aff ects loadings and can cause bunching. A critical aspect of running time analysis is that the scheduler is often being asked to simulta- neously resolve the opposing requirements of minimizing resources and maximizing on time performance. Providing maximum planned scheduling effi ciencies, combined with minimizing passenger travel times, can be in direct confl ict with providing achievable times for operators. It is also important to note that possibly the major determinant of transit system effi ciency is operating speed. The graph below provides a basic representation of the overall running time problem from a scheduling perspective. It shows a simple example for one route, indicating the steps as vehicle savings thresholds are achieved. This is an important element of the equation: savings are not linear, but are primarily a step function with costs increasing or decreasing in steps as vehicle requirements increase or decrease. What the scheduler should be moving towards when devel- oping running times is the point where effi ciencies are maximized and operating speeds high, but not to the point that degrades system reliability—represented by an area within the shaded area on the graph. This is, in theory, the point at which running times are “optimized,” and this point exists for each running time problem.

Chapter 3. Schedule Building 3-65 Level ͯ. Advanced Schedule Building How does a scheduler go about achieving these goals, and where are the potential pitfalls? Let’s look at the fi rst four goals in detail: ͭ. Accurate. As noted earlier in this chapter, the scheduler is trying to schedule for the “average” day that does not really exist. With the wealth of running time data provided by an AVL or APC system, however, he or she can come a little closer. A signifi cant problem is unexpected delays, caused by accidents, temporary street closings, wheel- chair boardings, and bicycle mountings and dismountings. One advantage of extensive running time data is that wheelchairs and bicycles are already accounted for in the data, even in cases of non-random occurrences (such as a route serving housing for people with disabilities or a college campus). If the standard deviation of the running time is small, then the use of average running time is logical. The more diffi cult situation is when there is considerable variation in running times. Under those circumstances, the use of an average results in lots of early trips and lots of late trips. ͮ. Realistic. This term can be more diffi cult to defi ne than is apparent at fi rst glance. An operator obviously wants a schedule that allows him/her to drive safely and arrive at time points on time. Operators also like the ability to take all of their scheduled layover time at the end of a route. However, operators diff er in their driving abilities and their ability to keep to schedule. Some observers have noted that “control of the door” is an important factor in an operator’s ability to keep to schedule, and variations in driver skill are also undeniable. It is not uncommon to see four runs on a route on time at all time points and a fi fth chronically late. Provision of suffi cient layover time is the most obvious means to control for diff erences among operators. The interaction between running times and layover will be discussed in more detail below. The scheduler’s ability to spot trends like this is important in the process of setting realistic running times. Some agencies also schedule mid-trip “holds” at transfer centers or major stops to help a route stay on schedule. This approach is often used for longer routes. Operators will adjust if they view a schedule as unrealistic. They may leave one terminal early, sacrifi cing layover time at this location to ensure a bigger chunk of layover time at the other terminal. If there is too much time in the schedule (in the late evening, for example), an operator may leave the terminal late knowing that s/he will “catch up” with the schedule later in the route. ͯ. Effi cient. As noted earlier, transit cost has a step progression—changes to running time have no impact on cost until an extra bus is required or can be removed, at which point the cost impact is large. The scheduler knows this as well as or better than anyone in the agency, and can make informed decisions regarding changes in running time and

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-66 layover time based on this knowledge. Ͱ. Running hot. One approach frequently used to avoid running hot is to schedule very tightly on the early segments of a route and provide more generous running time on later segments. This makes it almost impossible to run hot if an operator leaves on time, and yet gives the operator confi dence that s/he will be able to take all of the scheduled layover at the end of the trip. Another approach is to schedule very tightly on route segments and provide a more generous layover time. A major problem with this approach is accuracy for the customer. At stops along the early segments, the transit vehicle will almost always be a few minutes late. While this is certainly preferable to leaving early, it can create an impression of unreliability among riders, expressed in terms of “the bus is always late.” It can also leave the impression with the operator that the schedulers did not do an accurate job of establishing running time and the schedule cannot be reliably followed. At some time points, such as the end of the line, arriving early may be considered good for customer service. Why should the driver slow down when traffi c is light in a location where no passenger boardings are expected? Some agencies consider an early arrival at a route terminal to be on time. Agency policies may also aff ect running time. Policies mentioned in the survey included the requirements that all passengers be seated or that all strollers be folded before the operator leaves a stop. By increasing the dwell time at stops, these policies lengthen running time on all routes. Such policies may be implemented without a full consideration of potential costs. A brief math review may be appropriate before addressing running time strategies. This chap- ter has referred several times to “average” running times. Other useful concepts are “median” and “mode.” The median is the middle value in an ordered list of numbers. The mode is the most commonly occurring value in a group of numbers. As an example, consider the two sets of observations of running times on a given route seg- ment shown below. The scheduled running time for this segment is ͭͬ minutes. The fi rst set is very symmetrical, and the average, median, and mode are all identical. If we were to plot this set, it would look like a standard bell curve. The second set is asymmetrical, with one very low running time and several very high running times. Median and mode are not aff ected by extreme values, whereas the average is skewed (this is the reason why schedulers would eliminate outliers or extreme values before taking the aver- age). Also, there may be more than one mode in a given data set. While the average is the most familiar and widely used measure, the median value is a good choice for asymmetrical data sets.

Chapter 3. Schedule Building 3-67 Level ͯ. Advanced Schedule Building We have noted earlier in this manual the types of data that a scheduler uses. The variability of data, in both quantity and quality, is never more evident than when undertaking running times analysis. The best type of running time data is that which provides elapsed running time, both for end-to-end and trip segments. Using this type of data the scheduler can analyze and de- velop running times based on actual running time observations. It is of signifi cant value if the data identifi es long waiting periods along the route. This can identify either key bottlenecks, or locations where operators are waiting due to excessive running time. NEVER use schedule deviation data by itself as a means for identifying running time issues. Consider a smart operator who knows the route and running times. Knowing excessive running time exists, he/she leaves the trip terminal late to avoid running hot. This late trend continues along the route, until fi nally arriving on time. The outcome is a series of “late” running observa- tions that could suggest to the uninitiated a need for more running time, when the opposite is true. The reverse can hold true where operators leave early because they know that the scheduled running time is insuffi cient. Running time analysis requires elapsed running times to ensure meaningful outcomes! Running Time Observation 1 Running Time Observation 2 8 6 9 9 9 9 10 10 10 10 10 10 10 15 11 15 11 15 12 15 Average 10 11.4 Median 10 10 Mode 10 15

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-68 Running Time Strategies What is a scheduler to do? Here are strategies to set running times that have been adopted or proposed at various agencies. Some of these strategies have only become feasible with the advent of APC and AVL systems that provide large volumes of data. First, we should clarify that establishing diff erent running times at diff erent times of the day and on diff erent days of the week (weekday/Saturday/Sunday) is a standard practice at all but the smallest transit agencies in the survey. This is assumed as an ongoing practice and is not listed as a separate strategy, but one of the implications of diff ering running times is addressed below. Use of running time averages, leavened with professional judgment. This continues to be the most common approach among survey respondents to establishing running times. This is a good approach for routes with little variation (i.e., a small standard deviation) in running times. However in most cases the variation observed in running times is signifi cant. Diff erentiation by route segment. As discussed above, the strategies of setting minimal run- ning times along early segments of a route and either more generous running times in later segments or more generous layover time are used by many agencies to provide adequate running time while minimizing early departures at time points. If either of these approaches is used, the amount of time taken from initial route segments should be small, leaving a “tight” running time rather than an impossible one. Where a route has high seat turnover, key mid- point destinations, or midpoint connections, this approach can be less valuable. Use of speed (in miles per hour) to set or evaluate running times. The survey indicated that several agencies use expected or observed speeds to set running times. Some use posted speed limits and then factor the resulting running times to account for stops. Many schedulers check the reasonableness of scheduled running times for route segments by calculating the scheduled speed for each segment (segment distance divided by scheduled running time). Below is an example of a running time matrix with average speeds included. The scheduler made running time changes on Segments BC, CD, FG, and GH (highlighted), and is using calculated speeds to assess whether the proposed running times are realistic. Point C is the downtown terminal, so the lower scheduled speeds are logical. Point G is a regional mall, so lower speeds during hours of major activity at the mall (in the base and PM peak) are also reasonable.

Chapter 3. Schedule Building 3-69 Level ͯ. Advanced Schedule Building Distance Segment AM Peak Base PM Peak Night Time Speed Time Speed Time Speed Time Speed 2.83 AB 11 15.4 12 14.2 12 14.2 11 15.4 2.01 BC 11 11.0 11 11.0 11 11.0 8 15.1 0.99 CD 5 11.9 6 9.9 6 9.9 5 11.9 1.52 DE 8 11.4 9 10.1 9 10.1 7 13.0 2.15 EF 8 16.1 9 14.3 9 14.3 7 18.4 2.57 FG 11 14.0 13 11.9 13 11.9 9 17.1 3.80 GH 15 15.2 17 13.4 18 12.7 14 16.3 4.87 HI 20 14.6 19 15.4 20 14.6 16 18.3 1.81 IJ 7 15.5 6 18.1 6 18.1 6 18.1 22.55 Total 105 13.5 111 12.8 113 12.5 93 15.6 Use of percentiles in establishing running times. This strategy becomes possible with large amounts of running time data. One survey respondent reported setting running times on a route so that: Ͳͱ% of all trips fi nish in time for the operator to take the minimum layover. As an example, if the scheduled running time of a trip is ͱͭ minutes with nine minutes of scheduled layover and a contract stipulation of ͭͬ% minimum layover, then Ͳͱ% of trips are completed no more than three minutes late (to allow for the minimum six minutes layover time); ͵ͬ% of all trips fi nish in time for the operator to start the next trip on time. In this ex- ample, ͵ͬ% of all trips are completed no more than nine minutes late; ͭͬ% of all trips fi nish too late to start the next trip on time. Percentiles may not be familiar to all schedulers, so a brief refresher is useful. The value of the ͵ͬth percentile is a number that is equal to or greater than ͵ͬ% of all observations in the data set. Similarly, the Ͱͬth percentile is a number (lower than the ͵ͬth percentile) that is equal to or greater than Ͱͬ% of all observations. The ͱͬth percentile is the median. • • •

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-70 TCRP Report ͭͭͯ discusses how AVL-APC data can be used to set running times at the route and segment level.ͮ Route-level approaches include percentile-based strategies such as: Setting running time at the ʹͱth percentile of observed running times (in other words, running times are set so that ʹͱ% of all trips fi nish on time). Setting the one-way running time plus layover at the end of the one-way trip at the ͵ͱth percentile of observed running times and setting layover time at the diff erence between the the ͵ͱth and the ʹͱth percentile of observed running time (meaning that ʹͱ% of all trips fi nish on time and ͵ͱ% can start the next trip on time). TCRP Report ͭͭͯ notes that these strategies must be coupled with an operating practice of holding at time points, refl ecting a trade-off between on-time performance and travel speed. This trade-off is evaluated diff erently at diff erent agencies. The use of a high percentile means that running time will be relatively high. Many schedulers see high running times and holding at time points as fatal operational fl aws in the approach, arguing that you should never write a schedule that deliberately puts an operator in a position where he/she needs to hold at a time point. Many schedulers would favor use of a much lower percentile. TriMet is quoted in TCRP Report ͭͭͯ as suggesting a low percentile criterion because running early is more harmful to passen- gers than running late. As an example, segment-level running times can be set at the Ͱͬth percentile of observed cumulative (from the start of the line to a given time point) running time to guard against running hot. Another survey respondent in this study reported using the Ͳͬth percentile as a reasonable guide in setting running times. “Cumulative” is an important concept in establishing running times. Previous sections of this chapter emphasized setting running times at the route level and then distributing it appropri- ately across route segments. Taking the opposite approach of establishing running times for each segment and then aggregating for the entire route runs the risk of rounding errors and inaccurate overall route running time, especially as half-minute increments have fallen into disuse. This is a diff erent way, enabled by much greater availability of data, of thinking about running time. Scatter diagrams showing the distribution of running times for a given direction and segment (or for the route as a whole) allow the scheduler to see where the percentile lines fall and how these relate to the outliers. AVL/APC outputs can provide the raw data to construct scatter diagrams, and some computerized scheduling packages include modules that auto- matically create these diagrams. • • 2 Furth, P.G., B. Hemily, T.H.J. Muller, and J.G. Strathman. TCRP Report 113: Using Archived AVL-APC Data to Improve Transit Perfor- mance and Management. Transportation Research Board of the National Academies, Washington, D.C., 2006. See especially chapters 4 and 5.

Chapter 3. Schedule Building 3-71 Level ͯ. Advanced Schedule Building A real-world example of a scatter diagram is shown below, based on real observations from an AVL system (reproduced from the Hastus ATP system). Each dot represents an end-to-end running time observation, at a certain time of day. There are many days of data in this example and so the same trip may appear many times (as many dots), with the same or diff erent ob- served running times. The variation in running times is notable but not unusual. Scheduled running time is shown as a horizontal bar. ExisƟng Run Time Same trip varying over several days ExisƟng Run Time This example is explored at greater length in the Advanced Practices—Running Time and Layover discussion later in this section. The discussion highlights a lack of consensus at this point as to where to “draw the line” in using the percentile approach. Many schedulers favor use of a lower percentile, both to avoid running hot and to avoid unnecessary passenger delays as buses sit waiting for time through- out the system. The more important point here is to develop the ability to make practical use of the reams of data produced by APC/AVL systems. After a few sign-ups, the eff ect on sched- ule adherence of setting running times using X percentile will be apparent, at which point the scheduler may conclude that this approach works or may experiment with use of a diff erent percentile. The percentile approach is just one of many statistical means of developing running times. The use of percentiles is arguably simplistic in that it fails to grasp the variability of running times suffi ciently, nor does it allow for consideration of diff erent types of frequency distribution. Some agencies utilize tools that try to estimate a “least cost function,” where a large data set is included as input, and then various running time options are applied. The set of running times

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-72 that results in the lowest “cost” (determined based on applying costs to late or early running) is provided as the “optimal” output. The availability of larger volumes of data does not necessarily call for changes in traditional means of establishing running times. It does, however, allow more sophisticated models of running times analysis and development to be undertaken. One scheduler suggested that schedules based on (ͭ) the average running time from APC/AVL data less approximately two minutes for the fi rst segment and (ͮ) the average running times for all subsequent segments can increase on-time performance. Headway-based schedules. This strategy was employed in the implementation of Bus Rapid Transit (BRT) service in Los Angeles. Because a goal of BRT was to provide faster trips, no intermediate time points were initially established: the BRT bus would never be held at a time point. The buses would leave from the terminal every X minutes, and on-street supervision would assist in maintaining this spacing throughout the route. In scheduling terms, BRT buses were given free running time. While additional street supervision was an eff ective tactic in achieving consistent headways, intermediate time points were eventually introduced to aid in controlling the route and avoiding bus bunching. An AVL system could make a headway-based schedule functional, with extensive monitoring of current conditions along the route. The key here is the presence of eff ective street supervision at all points where buses may become bunched or be inordinately delayed. As AVL and APC systems become more established and the volume of available data increases exponentially from today, schedulers will experiment with various approaches to establish- ing running time. Multiple techniques may even be used at a single agency, depending on the variability in running time on a specifi c route. Continued experimentation with innovative ap- proaches will benefi t the industry as a whole. free running time The absence of a specifi ed running time along a given segment, with an estimated arrival time at the end of the segment. Frequently used on the express portion of an express bus trip, free running time is a com- ponent of headway-based sched- ules and is sometimes included on the last segment of a local route.

Chapter 3. Schedule Building 3-73 Level ͯ. Advanced Schedule Building Intertiming with Even and Uneven Headways In most transit systems, there is a corridor segment served by two (or more) otherwise unre- lated routes. Coordination of schedules along this segment can maximize the frequency of service. This process of schedule coordination is known as intertiming. Intertiming is easiest when both routes have the same headway. For example, if Route X and Route Y both have ͭͬ-minute headways, their schedules can be intertimed as follows: Route X Route Y :00 :05 :10 :15 :20 :25 The intertiming of the two routes provides a fi ve-minute headway along the route segment. When headways diff er, the scheduler must fi gure out a coordination scheme where both head- ways will fi t together without causing two trips to occur at the same time. Depending on the incompatibility of the two headways, one or more of the trips each hour (or however often the pattern repeats) may have to be moved to form an uneven headway on one of the routes. The scheme is developed fi rst for off -peak times. Service during peaks may be frequent enough so that coordination is neither feasible nor really necessary. For one example of combining and blending headways, consider the following: Route X oper- ates every ͭͱ minutes, at :ͬͱ, :ͮͬ, :ͯͱ and :ͱͬ past the hour. Route Y operates every ͮͬ minutes, at :ͭͬ, :ͯͬ and :ͱͬ past the hour. The obvious confl ict here is the two trips operating at :ͱͬ, plus other trips operating within fi ve minutes of each other. The simplest course of action is to move one of the :ͱͬ trips, but all this will accomplish is to give an uneven headway to one of the routes. To optimize the situation, both routes need to be intertimed. The combined routes of- fer seven trips per hour over the common segment, which works out to four trips on a ͵-minute headway and three trips on an eight minute frequency—an average ʹ.Ͳ-minute headway. But an even headway will not work, since there is a missing Y trip each hour which will leave a gap between a pair of X trips. One possible blending scheme is shown below. intertiming The process of scheduling trips of two or more routes that share a common segment in a manner that evenly spaces the trips over the common segment. Intertiming is intended to provide more frequent service for those passengers who begin and end their trips within the shared segment.

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-74 Route X Route Y :04 :10 :20 :29 :37 :47 :53 The blended headways vary from six to ten minutes, bunching around the missing Y trip. Though not perfect, the scheme does a credible job of spacing trips on the shared corridor segment as well as on the individual route segments. Of greater importance, it eliminates the wasteful practice of scheduling two trips together. Intertiming is most useful when the common segment is relatively long, there is extensive boarding and alighting activity, and many trip origins and destinations are along the common segment. If these conditions do not hold, then intertiming may not be necessary. A variation of blended headways is the merging of local and express service on the same route. In some cases the headways of the two services are the same, but the running time is diff erent. The concern in this situation is where on the line the vehicles should be evenly spaced versus where the express will pass the local. Depending on the length and other characteristics of the line, the scheduler may have only one point where the trips can be evenly spaced. That point will most likely be the max point. The point where the express vehicle passes the local vehicle is of less importance on bus routes. For rail or trolley coach routes without facilities for passing, the scheduler will have to be innovative, starting the express trip just ahead of the local and ap- plying running time (and possibly a headway adjustment) so the express does not catch up to the next local before the end of the route or the appropriate turnback location. Sometimes the scheduler deliberately wants the headway to be an uneven interval. The most common situation is when every other trip on a route turns short of the normal route end. Giv- ing the short-turn trips a wider headway can even out ridership levels between through and short-turn vehicles. For example, if a route has a seven- to eight-minute headway, the trips could be arranged to operate six and nine, with the nine-minute interval given to the short-turn trip, as shown below:

Chapter 3. Schedule Building 3-75 Level ͯ. Advanced Schedule Building Through Trip Short-turn :00 :09 :15 :24 :30 :39 :45 :54 Assuming random passenger arrivals, more passengers will be waiting for the short-turn ve- hicle, since they have nine minutes to gather at any given stop as opposed to six minutes for the through vehicle. This means that more passengers who can take either service will be on the short-turn vehicle, which should even out the loads between the two Two considerations apply to using uneven headways. First, the eff ect of moving a trip by a min- ute or two diminishes as the headway widens. Any headway over ͭͬ minutes probably would not benefi t from the adjustment. Second, fi ne tuning touches by the scheduler will be most eff ective with good street supervision to keep the trips from bunching. Finally, there is the issue of standardization of running times along the common segment. This issue may be addressed in the labor agreement, and it is a logical idea, but in certain circum- stances it may be the wrong idea. Reasons to avoid strict standardization include: diff erent dwell times on routes with diff erent destinations and ridership, and performance of diff erent bus types. Where standardization is enforced by computerized scheduling software, sched- ulers work around it when necessary by defi ning diff erent pairs of time points for diff erent routes. Advanced Practices—Running Times and Layover Previous running time discussions focused primarily on how best to set running times for a giv- en set of available data. The discussions alluded to but did not directly address the important interaction between running times and layover time. In “optimizing” running times it is wise to consider layover requirements and implications, in order to prepare the “best” schedule. In many cases, running time variations limit the scheduler’s capacity to set an “optimal” run time that results in high levels of on time running. Consider the following running time dia- gram, shown earlier and based on real observations from an AVL system (reproduced from the

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-76 Hastus ATP system). Each dot represents an end-to-end running time observation, at a certain time of day. There are many days of data in this example and so the same trip may appear many times (as many dots), with the same or diff erent observed running times. The exist- ing running time is shown as a line that changes across the day as the running time periods change. ExisƟng Run Time Same trip varying over several days ExisƟng Run Time In this example, there is little chance for the scheduler to develop any proposed running times that will result in a high level of on-time performance. The observations are simply too vari- able. In our experience this is not unusual, even for smaller systems without signifi cant conges- tion issues. There may or may not be an operational solution to the running time variability. The scheduler should bring this variability to the attention of operations staff , to see if resolution is possible. This brings us to an important point: not all running time problems are scheduling issues! Many transit systems fail to see this point and attempt to solve an operational or variability problem by changing scheduled running times. The outcome tends to be poor reliability and ineffi cient operations. In the above example the only way any reasonable form of reliability can be built into the schedule is through provision of suffi cient layover to allow “next trips” to depart on time. This is where joint consideration of running time and layover time comes into consideration. Inclusion of both running times and layover times in the optimization process is a necessary approach to maintaining operational reliability.

Chapter 3. Schedule Building 3-77 Level ͯ. Advanced Schedule Building In the above example the running time can arguably be set anywhere within a range from ͯͬ to ͯͳ minutes. For any running time within this range, there will be high levels of late and/or early running and probably only Ͱͬ-ͱͬ% “on time” (however it is defi ned). However, if we simulta- neously consider running time and layover time, we can at least ensure that the next trip can depart reliably and hopefully avoid the all-day cascading impact of late departures on on-time performance. An example using charts & data tables from the Hastus ATP system with a combination of graphical data views, statistical approaches, and scheduler experience can demonstrate how to develop a solution. The chart below shows the same data set of observed running times. The on-time range of one minute early to fi ve minutes late is indicated on the chart. The horizontal line represents existing running time, which changes across the day as the running time periods change. The percentage of trips within the “on time” category shows below the running time. A table of information about the observations is also provided. The “percent below run time” is the same as the percentile discussed in a previous section; in this case, running time is sched- uled at the Ͱͯrd or ͰͰth percentile. Note this is a large data set that covers multiple operating days. For this kind of analysis, the availability of AVL/APC systems allows this kind of rich data set to be used for more eff ective running time analysis. ExisƟng Run Time On Time ExisƟng Run Time

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-78 The scheduler is faced with a diffi cult assignment. Clearly there is major running time variabil- ity, and setting any run time at any level will not necessarily satisfy the aims described previ- ously. However, since we are charged with the responsibility of developing run times, we push on, and try to generate a proposed set of times. An automated method of “optimizing” on-time running, based on a basic mathematical model, is applied. The fi gure & table below indicate the outcome. Proposed Run Time On Time Proposed Run Time The scheduler (using the mathematical approach and then some manual manipulation) has done a reasonable job here of providing adequate running time without excessively slow- ing the service down. Note, however, that a large number of trips can potentially run early (those observations below the line). In fact between Ͳͬ% and ͳͬ% of observations fall below the proposed time (another way of saying that running time is scheduled at the Ͳͬth or ͳͬth percentile). In addition, there are still many trips that will not have enough running time (those

Chapter 3. Schedule Building 3-79 Level ͯ. Advanced Schedule Building observations above the line). The number of trips with “on time” running time, according to the table, is only around ͯͬ% to ͯͱ%. This is a reasonable solution, but is probably not optimal. What if we consider running time and layover time together? The goal is to set both at a level that allows a high percentage of on-time next trip departures. Transit agency policy may guide this decision or it may be totally up to the scheduler, based upon the individual transit system. The fi gure & table below show recovery plus layover times set at around the ͵ͯrd percentile. That is, if running time plus layover between ͮ PM and Ͳ PM is set at Ͱͭ minutes, ͵ͯ% of next trips will depart on time. The dots above the line are those that would depart the next trip late. Given the proposed running time of ͯͲ minutes, (see above), the layover time proposed would be fi ve minutes during this period. Using this approach, over ͵ͯ% of next trips will depart on time based upon the data set. Proposed Run Time + Layover Time (1-Way Cycle)

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-80 This is an appropriate point for the scheduler to consider if ͵ͯ% is suffi cient. It may be that a higher level is needed to ensure service reliability at policy levels for your system. In the exam- ple above, adding four additional minutes to the layover time, for a total of Ͱͱ minutes running time plus layover, would provide suffi cient time for all trips within the afternoon time period to depart the next trip on schedule. During this process, the trade-off between cost and reliability comes into play, and the skill and experience of the scheduler is required. By adding those extra four minutes (so a minimum layover of ͭͬ minutes) it may cost an additional vehicle. This then becomes a policy decision— would the transit system be prepared to incur the additional cost to achieve the additional ser- vice reliability? In real terms, the tradeoff comes down to ensuring a couple of additional trips departing on time versus the annual cost of an additional vehicle. There is of course no one answer to that question—it will vary by transit system—but it is fair to say that most agencies would accept a ͵ͯ% next-trip departure rate under these circumstances. When considering running time and layover time simultaneously, we are essentially determin- ing minimum layover. The scheduling limitations and round-trip cycles may result in higher- than-minimum-specifi ed layovers. In this example, at a Ͱͭ minute run time plus layover may actually end up as Ͱͱ minutes if the running time is the same in both directions, and the fre- quency is ͯͬ minutes. Layover requirements are discussed elsewhere in this manual. During that discussion, the concept of layover being a function of running time variability was noted. In an example like this one, layover is used as a means of dealing with run time variability, regardless of the level of running time being set, because for running time data with high variability, the scheduled running times cannot achieve the necessary reliability levels. In this example the running time could set at a much lower level, let’s say around the average of ͯͯ minutes. In that case, running time plus layover time would still be Ͱͭ minutes, and the minimum layover would be eight minutes. In many transit systems the graph above is representative of actual operations and running time variability is high. In this situation the joint consideration of running time and layover time is as important to the system reliability as the development of running times. How Many Running Time Periods? The number of running time periods can determine how reliable a schedule is. In theory, more periods result in better on-time performance.

Chapter 3. Schedule Building 3-81 Level ͯ. Advanced Schedule Building However, this comes at a cost to the simplicity of the schedule. In the extreme, a single all-day running time period allows a simple all-day headway to be developed. Conversely, changing running times results in more complex schedules, where the clock face can only be maintained during specifi c time periods. Where running times change dramatically and often, the headway is compromised, since successive trips have diff erent running times and the headway is diff er- ent at various time points along the route. There is no “right” answer. The scheduler needs to be guided by the data and the analysis. In many cases, the analysis tool can recommend running times periods. As with many “tools,” the scheduler must realize that the mathematical answer is not necessarily the best operational answer, and fewer running time periods may be warranted. Take the two examples below. The shape of the data indicates immediately that only a few run- ning time periods are needed for the example on the left, whereas a range of time periods are needed for the example on the right, to refl ect the changing running time trends. In cases where running time variability is high enough that a range of running times can be applied with similar outcomes to the same data set, adding additional running time periods is not worth the complexity, as estimating run times to such a level of precision is optimistic. The recommendation is not to overuse running time periods. Having noted this, however, it is likely that for most transit routes operations will be faster late at night, early in the morning, and during some weekend periods. These trends should be refl ected in the running times. As with all aspects of scheduling the scheduler should be guided by experience, common sense, and good operations principles when deciding on how many running time periods are required for a route.

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-82 Transitioning of Running Time Periods A second aspect of the number of running time periods relates to how running period transi- tions are handled. The intermediate section of this chapter discussed transitions, but the topic deserves further attention here. Let’s start with a simple example—one route with several running time transitions during the AM Peak. The run times are set out below. 5:00 6:00 7:00 8:30 9:30 to to to to to 5 :59 6:59 8:29 9:29 14:59 A - - - - - B 5 7 8 7 6 C 8 9 10 9 9 D 7 8 10 8 7 E 6 7 9 7 7 T ota l 26 31 37 31 29 Note that the peak period time rises quite steeply. This example illustrates the problems that such running time changes may pose. A schedule is provided below, based upon the proposed running time periods. A B C D E Run Time 5:55 6:00 6:08 6:15 6:21 26 6:15 6:22 6:31 6:39 6:46 31 6:30 6:37 6:46 6:54 7:01 31 6:45 6:52 7:01 7:09 7:16 31 7:00 7:08 7:18 7:28 7:37 37 7:15 7:23 7:33 7:43 7:52 37 7:30 7:38 7:48 7:58 8:07 37 7:45 7:53 8:03 8:13 8:22 37 8:00 8:08 8:18 8:28 8:37 37 8:15 8:23 8:33 8:43 8:52 37

Chapter 3. Schedule Building 3-83 Level ͯ. Advanced Schedule Building A B C D E Run Time 8:30 8:37 8:46 8:54 9:01 31 8:50 8:57 9:06 9:14 9:21 31 9:10 9:17 9:26 9:34 9:41 31 9:40 9:46 9:55 10:02 10:09 29 10:10 10:16 10:25 10:32 10:39 29 Note that the relatively large running time changes results in a compromised headway. For example, the run time increase at ͳ AM results in a ͭ͵-minute headway at Point D, yet the pre- scribed headway is ͭͱ minutes. Conversely, as running times are reduced at the end of the peak a short nine-minute headway occurs at Point E. Such schedules can result in unstable operation and probably do not refl ect “real-life” operating conditions. It is unlikely that the running time increases by six minutes between Ͳ:ͱ͵ AM and ͳ:ͬͬ AM. Instead this increase is likely to be a transition over a few trips, as traffi c and patronage increase. The scheduler should fi ne-tune the schedule accordingly. An updated example, with transi- tioned times, is provided below. The trips that have been “smoothed,” with non-standard run- ning times, are highlighted. 2910:0910:029:559:469:40 319:419:349:269:179:10 319:219:149:068:578:50 339:038:558:468:378:30 358:508:418:328:228:15 378:378:288:188:088:00 378:228:138:037:537:45 378:077:587:487:387:30 377:527:437:337:237:15 357:357:267:177:077:00 337:187:107:016:526:45 317:016:546:466:376:30 296:446:376:296:216:15 266:216:156:086:005:55 R un T im eEDCBA

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-84 To undertake this type of transitioning successfully requires a skilled scheduler with under- standing of local conditions and operations. Smoothing of Running Time Periods A more sophisticated method of transitioning, known as running time smoothing, can also be applied. This type of transitioning recognizes that running times tend to change less in a tidal movement along a route, and more across the entire route at the same time. The running time periods apply not to the start time of the trip (as in traditional methods), but anywhere along the route that a trip may be at that time. The trip then immediately transitions to the next period. This is shown diagrammatically below, for the ͱ:ͱͱ AM trip. The process eff ectively shifts the trip into the Ͳ:ͬͬ-Ͳ:ͱ͵ running time period as soon as it hits Ͳ:ͬͬ AM, regardless of where it is along the route. The ͱ:ͱͱ AM trips ends up with a total of ͮ͵ minutes running time (ͱ + ͵ + ʹ + ͳ) in this instance. 5:00 6:00 7:00 8:30 9:30 to to to to to 5 :59 6:59 8:29 9:29 14:59 A - - - - - B 5 7 8 7 6 C 8 9 10 9 9 D 7 8 10 8 7 E 6 7 9 7 7 T ota l 26 31 37 31 29 Applying the same running time periods to the same trips, but with smoothed periods, would result in the schedule below. The shading indicates that a given trip has moved into the next running time period.

Chapter 3. Schedule Building 3-85 Level ͯ. Advanced Schedule Building 2910:3910:3210:2510:1610:10 2910:0910:029:559:469:40 319:419:349:269:179:10 319:219:149:068:578:50 319:018:548:468:378:30 338:488:418:338:238:15 378:378:288:188:088:00 378:228:138:037:537:45 378:077:587:487:387:30 377:527:437:337:237:15 377:377:287:187:087:00 357:207:117:016:526:45 317:016:546:466:376:30 316:466:396:316:226:15 316:266:196:116:025:55 R un T im eEDCBA This approach automatically applies running time transitioning. It can be useful on long routes with signifi cant running time changes, and often better refl ects realistic operating conditions. In cases where there are large peak-direction traffi c and passenger movements (typical of downtown-based services), this approach should be used with caution. Running Time Myths To summarize this discussion, some common scheduling myths are noted below: Running time problems are all scheduling problems. High variability of running times indicates a strong possibility that there are other factors at work and scheduling solu- tions alone cannot resolve the issue. In these cases the scheduler should identify the is- sues and work with operations staff to clarify what can be resolved at a scheduling level and what needs to be addressed at an operating level. This is often not an easy process and requires strong cooperation between scheduling and operations staff . •

Level ͯ. Advanced Schedule BuildingChapter 3. Schedule Building 3-86 Lower on-time performance means insuffi cient running time. In many cases early running may be as big an issue as late running. In other cases, running time may not be the issue at all. Late running observations automatically mean that additional running time is required. Operators adjust for the conditions they regularly experience. Therefore if scheduled running time is excessive, they may leave the terminal late to avoid running hot, resulting in late running observations along the route. The same applies in reverse. This is an example of the danger of using point checks or schedule adherence data as primary sources for running time adjustments. Schedule deviation data can be used as a means of setting running times. This is a broader statement of the previous two myths. Exception data is just that—data show- ing exceptions and deviations. Only elapsed running times can be used to analyze and revise running times. This cannot be stressed strongly enough. Layover requirements are solely a function of trip length. The length of a route does not necessarily indicate the need for more layover for schedule adherence purposes. Running time variability is not necessarily a function of route length, but of “typical” operating factors such as traffi c congestion, patronage, operator variability, etc. Often (but not always) on longer routes, there is a “quiet” patch where the operator has a chance to make up lost time. Where longer layover is suggested for longer routes it is primarily related to operator rest time, not necessarily to run time variability. Setting running times is a statistical process. Many statistical and modeling ap- proaches have been applied to running times. Often these approaches estimate the impacts of new running times based on existing data. However, these approaches fail to recognize an important consideration: scheduled running times infl uence operating running times and therefore one cannot simply apply a statistical approach and esti- mate outcomes. Statistical methods must be combined with local knowledge, visual presentation of data, and scheduler experience and skills to provide the “optimal” outcomes. In one city an automated AVL system that “reminded” operators running early or late was turned off , and run time data were collected. The results indicated sig- nifi cant running time diff erences when operators were not required to meet scheduled times. This phenomenon is also supported by the Los Angeles Metro Rapid experience with free running time. A fi nal point to note that can be overlooked even by the most experienced schedulers is to always calculate and review check operating speeds when proposed running times have been developed. This is the fi nal “common sense” check of the type that schedulers should always be looking to apply to all aspects of the scheduling process. • • • • •

Chapter 3. Schedule Building 3-87 Level ͯ. Advanced Schedule Building LEVEL 3B End of Schedule Building Schedule Blocking continues on the next page.

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TRB’s Transit Cooperative Research Program (TCRP) Report 135: Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling explores information on available scheduling tools and techniques and their capabilities. Also, the report provides guidance to transit agencies on a variety of scheduling issues typically faced in a transit operating environment.

TCRP Report 135 is an update to TCRP Report 30: Transit Scheduling: Basic and Advanced Manuals and addresses contemporary issues in transit scheduling. The appendixes to TCRP Report 135 were published as TCRP Web-Only Document 45: Appendixes to TCRP Report 135: Controlling System Costs: Basic and Advanced Scheduling Manuals and Contemporary Issues in Transit Scheduling.

An interactive scheduling manual is available as an ISO image. Links to the ISO image and instructions for burning a CD-ROM from an ISO image are provided below. Once a CD-ROM has been made with the ISO image, open the folder on the CD-ROM called Interactive Scheduling Manual and click on Transit_Scheduling_Lessons.pps.

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