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Level . Advanced Schedule Building Chapter 3. Schedule Building 3.5 Advanced Topics In Schedule Writing Establishing Running Times LEVEL 3B 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 % 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 efficient operation. The scheduler has a direct impact on operational costs and, by minimizing unproductive time, can enhance efficiency. . To avoid instances of running hot, a major transgression in transit operations. . To eliminate or sharply reduce situations where running time is too tight and service runs late or is subject to buses bunching. . To maximize on-time performance. As discussed in the intermediate section of this chapter, each agency has a specific definition of "on time." Typically, a trip is considered on time if it arrives or departs from a time point within to 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. 3-63

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Chapter 3. Schedule Building Level . Advanced Schedule Building The impact of running times can be a significant factor in unreliable operations, particularly with regard to bunching of vehicles. While bunching is often caused by varying operating con- ditions (traffic, congestion, loading variability, etc.) the scheduled run times can affect whether vehicles operate early or late. And once vehicles fall outside the schedule, this affects 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 efficiencies, combined with minimizing passenger travel times, can be in direct conflict with providing achievable times for operators. It is also important to note that possibly the major determinant of transit system efficiency 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 efficiencies 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. 3-64

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Level . Advanced Schedule Building Chapter 3. Schedule Building How does a scheduler go about achieving these goals, and where are the potential pitfalls? Let's look at the first 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 significant 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 difficult 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 difficult to define than is apparent at first 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 differ 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 fifth chronically late. Provision of sufficient layover time is the most obvious means to control for differences 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, sacrificing 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. . Efficient. 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 3-65

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Chapter 3. Schedule Building Level . Advanced Schedule Building layover time based on this knowledge. . 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 confidence 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 traffic 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 affect 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 first 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 affected 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. 3-66

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Level . Advanced Schedule Building Chapter 3. 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 significant value if the data identifies 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 finally 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 insufficient. Running time analysis requires elapsed running times to ensure meaningful outcomes! Running Time Running Time Observation 1 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 3-67

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Chapter 3. Schedule Building Level . Advanced Schedule Building 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 different running times at different times of the day and on different 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 differing 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 significant. Differentiation 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. 3-68

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Level . Advanced Schedule Building Chapter 3. Schedule Building AM Peak Base PM Peak Night Distance Segment 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: % of all trips finish in time for the operator to take the minimum layover. As an example, if the scheduled running time of a trip is minutes with nine minutes of scheduled layover and a contract stipulation of % minimum layover, then % of trips are completed no more than three minutes late (to allow for the minimum six minutes layover time); % of all trips finish 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 finish 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 th percentile is a number (lower than the th percentile) that is equal to or greater than % of all observations. The th percentile is the median. 3-69

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Chapter 3. Schedule Building Level . Advanced Schedule Building 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 th percentile of observed running times (in other words, running times are set so that % of all trips finish on time). Setting the one-way running time plus layover at the end of the one-way trip at the th percentile of observed running times and setting layover time at the difference between the the th and the th percentile of observed running time (meaning that % of all trips finish on time and % 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, reflecting a trade-off between on-time performance and travel speed. This trade-off is evaluated differently at different 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 flaws 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 th 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 th 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 different 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. 3-70

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Level . Advanced Schedule Building Chapter 3. 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 different ob- served running times. The variation in running times is notable but not unusual. Scheduled running time is shown as a horizontal bar. Same trip varying over several days Exisng Run Time Exisng 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 effect 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 different 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 sufficiently, nor does it allow for consideration of different 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 3-71

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Chapter 3. Schedule Building Level . Advanced Schedule Building 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 first 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 free running time point. The buses would leave from the terminal every X minutes, and on-street supervision The absence of a specified running would assist in maintaining this spacing throughout the route. In scheduling terms, BRT buses time along a given segment, with an were given free running time. While additional street supervision was an effective tactic in estimated arrival time at the end of achieving consistent headways, intermediate time points were eventually introduced to aid in the segment. Frequently used on controlling the route and avoiding bus bunching. An AVL system could make a headway-based the express portion of an express schedule functional, with extensive monitoring of current conditions along the route. The bus trip, free running time is a com- key here is the presence of effective street supervision at all points where buses may become ponent of headway-based sched- bunched or be inordinately delayed. ules and is sometimes included on the last segment of a local route. 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 specific route. Continued experimentation with innovative ap- proaches will benefit the industry as a whole. 3-72

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Level . Advanced Schedule Building Chapter 3. 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 intertiming :20 :25 The process of scheduling trips of The intertiming of the two routes provides a five-minute headway along the route segment. two or more routes that share a When headways differ, the scheduler must figure out a coordination scheme where both head- common segment in a manner that ways will fit together without causing two trips to occur at the same time. Depending on the evenly spaces the trips over the incompatibility of the two headways, one or more of the trips each hour (or however often the common segment. Intertiming is intended to provide more frequent pattern repeats) may have to be moved to form an uneven headway on one of the routes. The service for those passengers who scheme is developed first for off-peak times. Service during peaks may be frequent enough so begin and end their trips within the that coordination is neither feasible nor really necessary. shared segment. For one example of combining and blending headways, consider the following: Route X oper- ates every minutes, at : , : , : and : past the hour. Route Y operates every minutes, at : , : and : past the hour. The obvious conflict here is the two trips operating at : , plus other trips operating within five minutes of each other. The simplest course of action is to move one of the : 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 . -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. 3-73

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Chapter 3. Schedule Building Level . Advanced Schedule Building The scheduler is faced with a difficult 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 figure & table below indicate the outcome. On Time Proposed Run 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 % and % of observations fall below the proposed time (another way of saying that running time is scheduled at the th or th percentile). In addition, there are still many trips that will not have enough running time (those 3-78

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Level . Advanced Schedule Building Chapter 3. Schedule Building observations above the line). The number of trips with "on time" running time, according to the table, is only around % to %. 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 figure & table below show recovery plus layover times set at around the rd percentile. That is, if running time plus layover between PM and PM is set at 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 minutes, (see above), the layover time proposed would be five 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) 3-79

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Chapter 3. Schedule Building Level . Advanced Schedule Building This is an appropriate point for the scheduler to consider if % is sufficient. 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 minutes running time plus layover, would provide sufficient 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-specified layovers. In this example, at a minute run time plus layover may actually end up as 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 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. 3-80

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Level . Advanced Schedule Building Chapter 3. 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 specific time periods. Where running times change dramatically and often, the headway is compromised, since successive trips have different running times and the headway is differ- 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 reflect 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 reflected 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. 3-81

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Chapter 3. Schedule Building Level . Advanced Schedule Building 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 o tal 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 3-82

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Level . Advanced Schedule Building Chapter 3. 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 AM results in a -minute headway at Point D, yet the pre- scribed headway is 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 reflect "real-life" operating conditions. It is unlikely that the running time increases by six minutes between : AM and : AM. Instead this increase is likely to be a transition over a few trips, as traffic and patronage increase. The scheduler should fine-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. R un A B C D E T im e 5:55 6:00 6:08 6:15 6:21 26 6:15 6:21 6:29 6:37 6:44 29 6:30 6:37 6:46 6:54 7:01 31 6:45 6:52 7:01 7:10 7:18 33 7:00 7:07 7:17 7:26 7:35 35 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 8:22 8:32 8:41 8:50 35 8:30 8:37 8:46 8:55 9:03 33 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 3-83

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Chapter 3. Schedule Building Level . Advanced Schedule Building 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 : AM trip. The process effectively shifts the trip into the : - : running time period as soon as it hits : AM, regardless of where it is along the route. The : AM trips ends up with a total of minutes running time ( + + + ) 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 o tal 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. 3-84

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Level . Advanced Schedule Building Chapter 3. Schedule Building R un A B C D E T im e 5:55 6:02 6:11 6:19 6:26 31 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 7:11 7:20 35 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 8:41 8:48 33 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 This approach automatically applies running time transitioning. It can be useful on long routes with significant running time changes, and often better reflects realistic operating conditions. In cases where there are large peak-direction traffic 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. 3-85

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Chapter 3. Schedule Building Level . Advanced Schedule Building Lower on-time performance means insufficient 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 traffic 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 influence 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- nificant running time differences 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 final 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 final "common sense" check of the type that schedulers should always be looking to apply to all aspects of the scheduling process. 3-86

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

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