Using Archived AVL-APC Data to Improve Transit Performance and Management (2006)

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45 Poor service reliability affects both passenger waiting time and crowding. However, traditional methods of analyzing passenger waiting time and crowding, developed in the data-poor age before AVL and APCs, do not account well for the impacts of irregularity upon passenger experience with respect to crowding and waiting time. This chapter presents some methods for analyzing waiting time using AVL data; the next chapter presents methods for analyzing crowding using APC data. These methods have been applied in spreadsheet files, which serve as prototypes of analysis tools that can be applied in AVL-APC data analysis soft- ware. (The spreadsheet files are available on the project description web page for TCRP Project H-28 on the TRB website: www.trb.org.) 6.1 A Framework for Analyzing Waiting Time The researchers developed a new framework for analyzing waiting time, one that accounts for how uncertainty in head- way and schedule deviation affects not only how long passen- gers wait on the platform, but also how much time they have to budget for waiting. That framework is described with mathe- matical justification in Furth and Miller (8). This section out- lines the framework’s main features. Then, they are applied to short-headway service in Section 6.2 and to long-headway service in Section 6.3. 6.1.1 Platform Waiting Time AVL captures data on headways and bus departure times. By making reasonable assumptions about when passengers arrive, and assuming the first bus is not too full for them to board, mean waiting time and the distribution of waiting time can be determined. “Platform waiting time” is the term used for the time passengers actually spend waiting at a stop. 6.1.2 Budgeted and Potential Waiting Time AVL data can also be used to estimate how long passengers have to budget for waiting. To have a small probability of arriving late at their destination, passengers must plan on waiting longer than the average platform waiting time. While passengers vary in their willingness to accept the risk of arriv- ing late at their destination, a reasonable working assumption is that passengers will accept a 5% risk of arriving late. There- fore, the 95th-percentile waiting time can be interpreted as budgeted waiting time. Budgeted waiting time can be divided into two parts: the part that passengers actually spend waiting and the remainder, called “potential waiting time.” For example, if a passenger budgets 10 min for waiting, but the bus arrives after only 4 min, the 6-min difference is the potential waiting time. Potential waiting time is not spent on the platform; it is spent at the des- tination end of the trip, where the traveler will arrive 6 min earlier than budgeted. However, because it was set aside for waiting, that time cannot be used as freely as if it had not been so encumbered; therefore, it still represents a cost to passengers. For example, passengers going to work in the morning could not spend their potential waiting time sleeping a few minutes later or staying at home with the kids a few minutes longer. Potential waiting time is a hidden cost associated with waiting, manifested in passengers having to start their trips earlier than they would otherwise have to if waiting time were certain. 6.1.3 Equivalent Waiting Time Equivalent waiting time is a weighted sum of platform and potential waiting time that expresses passengers’ waiting cost in equivalent minutes of platform waiting time. If the weight given to potential waiting time is 0.5, equivalent waiting time is given by W W Wequivalent platform potential= + 0 5.  C H A P T E R 6 Tools for Analyzing Waiting Time

The coefficient 0.5 expresses the cost of a minute of potential waiting time in terms of platform waiting time. Ideally, this parameter value should be estimated based on market research into traveler behavior and preferences. However, 0.5 is a rea- sonable value consistent with the body of travel demand research (8), lying between 0 (it has a real cost) and 1 (its unit cost should be less than that of platform waiting), and large enough to explain part of the reason that demand models typ- ically assign large relative coefficients to waiting time. When the unit cost of potential waiting time is 0.5, average equivalent waiting time can also be expressed as the average of mean platform time and budgeted waiting time: where W0.95 is the 95th-percentile waiting time. 6.1.4 Service Reliability and Waiting Time The transit industry has lacked a measure of service relia- bility that is measured in terms of its impact on customers. Traditional measures of service reliability such as coefficient of variation (cv) of headway and percentage of on-time depar- tures are valid descriptors of operational quality, but they do not express reliability’s impact on passengers. For example, how much is it worth to passengers to reduce the headway cv from 0.3 to 0.2, or to improve schedule adherence from 80% to 90%? Because a method of measuring reliability’s impact on passengers has been lacking, waiting time has been under- estimated, and service reliability undervalued. Poor service reliability affects passengers mainly by (1) mak- ing them wait longer and (2) making them have to budget more time for waiting. (It can also cause crowding, but that is something that can be measured directly.) Equivalent waiting time is a measure that accounts for both of those impacts. Because it includes budgeted waiting time, it is particularly sensitive to service reliability. It is measured in minutes of pas- senger waiting time, something that can be economically eval- uated and compared with, for example, the cost of improving service reliability, or the cost of a headway reduction as an alternative means of reducing passengers’ waiting time. 6.1.5 Ideal and Excess Waiting Time Passenger waiting time can be divided into two parts: ideal and excess. Ideal waiting time is the average waiting time that would result from service exactly following the schedule (35); excess waiting time is the difference between actual and ideal waiting time and is, therefore, the component of waiting time that can be attributed to operational issues. Separating excess from ideal waiting time provides a good idea of the quality of operations and the extent to which passenger service could be improved by improving service reliability. Excess waiting time W W Wequivalent platform= +( )0 5 0 95. . is also a good measure to use for evaluating contracted ser- vice, where the contractor is responsible for operations but not planning; Transport for London uses this measure with its contract bus operators. Excess waiting time can be a negative value; such a situa- tion could occur, for example, if more service is operated than scheduled. Until now, the concept of ideal and excess has been applied only to mean waiting time; however, it also applies to budgeted and equivalent waiting time, as the following sections show. 6.2 Short-Headway Waiting Time Analysis 6.2.1 Distribution of Waiting Time For transit service with short headways, passengers can be assumed to arrive independent of the schedule, effectively in a uniform fashion. If passengers are also assumed to depart with the first vehicle departure after their arrival (i.e., assuming there are no pass-ups), the complete distribution of waiting time can be determined from the set of observed headways. This determination is a step beyond the well-known formula for mean waiting time: where E[W] and E[H] are mean waiting time and mean head- way, respectively, and cvH is the coefficient of variation of head- way, which is the standard deviation of headway divided by the mean. (When applying this formula to a set of observed head- ways, one should use the “population standard deviation,” dividing by n = number of observations, rather than sample standard deviation, which divides by n − 1). Furth and Muller (8) explain how the distribution of passenger waiting time can be derived for both a theoretical headway distribution and for an arbitrary set of observed headways determined from AVL data. The method is best explained by an example. Suppose a route’s scheduled head- way is 8 min, and six buses were observed with the following headways (in minutes): With those headways, assuming passengers arrive at random and board the first bus, the waiting time distribution is as shown in Figure 12. At each observed headway, the waiting time distribution steps down in equal steps. Also shown for comparison is the ideal waiting time distribution (i.e., the waiting time distribution that would occur if service had per- fectly regular 8-min headways). In a waiting time distribution, the 95th-percentile waiting time is the value on the horizontal axis that divides the wait- Example 1 observed headways : { , , , , ,4 5 7 9 10 13} minutes E EW H cvH[ ] = [ ] +( )0 5 1 12. ( ) 46

ple, for which scheduled headways in the period of interest are not all equal: With Example 2, two datasets of 100 observed headways each are compared: Case a, with high irregularity (headway cv = 0.52), and Case b, with low irregularity (headway cv = 0.26). (Actual data values can be found in the spreadsheet file on the project description web page for TCRP Project H-28 on the TRB website: www.trb.org.) The waiting time summary in Fig- ure 14 shows that, with the reduction in irregularity, mean plat- form waiting falls only a little, from 5.1 to 4.3 min; budgeted waiting time falls much more, from 12.0 to 9.0 min. Combin- ing these waiting components under the composite measure equivalent waiting time shows that the reduction in irregular- ity saves passengers the equivalent of 1.9 min of waiting time— a result that, if service reliability were not accounted for, would require a headway reduction of almost 4 min, an action that would double operating cost. This example illustrates how the measures budgeted wait- ing time and equivalent waiting time reflect the impact of service reliability on passengers. 6.2.3 Percentage of Passengers with Excessive Waiting Times A second useful reporting format shows the percentage of passengers in various waiting time ranges or “bins.” This for- mat can be used to support a service quality standard such as “no more than 5% of passengers should have to wait longer than (scheduled headway + 2) minutes.”In its program for cer- tifying bus service quality, the French quality institute AFNOR Certification applies a standard in this format (36). Transit agencies in Paris, Brussels, and Lyon are among those with at least some bus lines certified under this standard. Example 2 scheduled headways: {5, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9} minutes 47 0 2 4 6 8 10 12 14 waiting time (min) actual ideal Figure 12. Passenger waiting time distribution for Example 1. 0.00 2.00 4.00 6.00 8.00 10.00 12.00 actual waiting ideal waiting excess waiting budgeted waiting time equivalent waiting time platform waiting time (values represented by cumulative heights) Figure 13. Passenger waiting time summary for Example 1. ing time distribution into two parts, with 95% of the area to the left and 5% to the right. For Example 1, the 95th-percentile waiting time equals 10.6 min for the actual headway distribu- tion; for the ideal headway distribution, 95th-percentile wait- ing equals 7.6 min. 6.2.2 Waiting Time Summary While the graph of the distribution of waiting time helps explain the relationship between headways and waiting time, it is not a useful format for management reporting or service quality monitoring. Two other formats are therefore offered. The first format for summarizing passengers’ waiting time experience is a summary of platform, budgeted, and equiva- lent waiting time, as shown in Figure 13. Optionally, the user can show how waiting time breaks out between ideal and excess waiting time. For example, the 10.6 min of budgeted waiting time divides into an ideal budgeted waiting time of 7.6 min and an excess budgeted waiting time of 3.0 min. Like- wise, equivalent waiting time, being 7.6 min, divides into ideal and excess parts of 5.8 and 1.8 min, respectively. Therefore, irregularity on this route costs passengers the equivalent of 1.8 min of waiting time. This format can also be used in a before–after comparison, as shown in Figure 14. Figure 14 is based on a different exam- 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 actual waiting, case a actual waiting, case b budgeted waiting time equivalent waiting time platform waiting time (values in minutes, represented by cumulative heights) Figure 14. Passenger waiting time comparison for Example 2.

Calculations for the Example 1 headway data are shown in Table 5. These calculations use a three-bin format, with thresh- olds of 9 and 11 min, which are 1 min and 3 min beyond the scheduled headway, respectively; the waiting times represented by these bins might be interpreted as “normal,”“excessive,”and “unacceptable.” The last observed headway in the table, which is 13 min long, best illustrates the calculation. Of the passen- gers arriving during the 13 min, those arriving in the first 2 min of the headway wait 11 min or longer; those arriving in the next 2 min wait 9 to 11 min; and those arriving in the last 9 min wait between 0 and 9 min. Overall, this table shows that 4.2% of passengers wait longer than 11 min. This format can also offer insights when comparing wait- ing time distributions. Table 6 compares the percentage of passengers with excessive and unacceptable waiting times for Example 2, Cases a and b. As Table 6 shows, the improved reg- ularity of Case b has dramatically reduced the percentage of passengers with excessive and unacceptable waiting times. 6.3 Long-Headway Waiting Time Analysis For routes with long headways, most passengers time their arrival at the platform to make a targeted departure. Sched- ule adherence or schedule deviation is critical to determining passengers’ waiting time. Let V equal the schedule deviation of the trip a passenger is trying to meet, defined by Early departures are represented by negative values of V. As long as schedule deviations are small compared to the scheduled headway, the number of passengers using a given trip will be independent of its schedule deviation or headway. Therefore, unlike with short-headway service, the experience of passengers is the same as the “experience” of buses (i.e., if 15% of the buses were late, it is fair to say that 15% of the pas- sengers had to wait for buses that were running late). V = −departure time scheduled departure time Therefore, distribution of schedule deviation is a measure of operational performance that relates closely with passenger experience. For interpreting schedule adherence as passenger experience, it is helpful to distribute schedule deviations into more than just the traditional three bins of “early,” “on time,” and “late.” For example, the user might specify thresholds at −1, 0, 3, 5, and 10 min and determine the percentage of trips, and therefore the percentage of passengers experiencing trips, in bins interpreted as unacceptably early, less than a minute early, on time (0 to 3 min), a little late, quite late, and unacceptably late. As valuable a measure as schedule adherence is, it still does not express an impact on passengers. The researchers were able to extend the waiting time framework to long-headway service in order to determine how much excess waiting time is caused by service unreliability. 6.3.1 Waiting Time Components Passengers are assumed to have a target arrival time and to arrive at or before this time. The target is set to give passengers a very low probability of missing the bus. Therefore, the target is an extreme value at the lower end of the schedule deviation distribution; the researchers use the 2nd-percentile schedule deviation (V0.02), meaning the time by which only 2% of buses will have already departed. Passengers following this policy will miss the bus once every 50 trips, or less (depending on how long before the target they arrive). Two components of waiting time are not avoidable and are, therefore, part of ideal waiting time, not excess waiting time. Because they depend only on the planned headway, they are not a subject of AVL data analysis; nevertheless, for com- pleteness, they are mentioned here: • Schedule inconvenience: a well-known form of hidden waiting time that arises from departures or arrivals not being scheduled when passengers want to travel. It is man- ifested in passengers who are going to work arriving before their work start time because the next bus would get them there too late. Likewise, after work, passengers may consis- tently have time to kill between leaving work and the next scheduled departure. • Synchronization time: the cost, in equivalent minutes of waiting, of ensuring that one is at the station by the target arrival time. To be sure of hitting that target, many passen- 48 Waiting Time (Bin Width) Normal 0 to 9 min (9 min) Excessive 9+ to 11 min (2 min) Unaccept. > 11 min (1000 min) Headway Total 4.0 4.0 4.0 5.0 5.0 5.0 7.0 7.0 7.0 9.0 9.0 9.0 10.0 9.0 1.0 10.0 13.0 9.0 2.0 2.0 13.0 Total 43.0 3.0 2.0 48.0 Percentage 89.5% 6.3% 4.2% 100% Table 5. Excessive waiting time calculation. Waiting Time Normal 0 to 9 min Excessive 9+ to 11 min Unaccept. > 11 min Case Total a 84.1% 8.2% 7.7% 100% b 94.8% 4.4% 0.8% 100% Table 6. Passenger waiting time distribution for Example 2.

gers will arrive early because of uncertainty in access time, the limits of human punctuality, and risk aversion. The waiting time between when passengers arrive and the ideal arrival time is part of synchronization time. Schedule inconvenience and synchronization time are unavoidable; they can be “blamed” on planning, as they are the inevitable consequence of designing a service with a long headway. In contrast, random waiting time that occurs after the ideal arrival time is due to service unreliability and is, therefore, excess waiting time. Its components, and their relation to schedule deviations, are shown in Figure 15. Excess platform waiting runs from the passengers’ target arrival time to the bus’s actual departure time. Excess bud- geted waiting time runs from the target arrival time to the 95th-percentile schedule deviation (V0.95). As in the case of short-headway waiting, passengers cannot plan on being picked up at the average departure time; they have to budget for an extreme value. The researchers assume they budget for the 95th-percentile schedule deviation; with that value, passengers will arrive late 5% of the time. Excess budgeted waiting time, being the spread in the sched- ule deviation distribution between V0.02 and V0.95, can be thought of as the time between the earliest likely and latest likely departure times.The greater the service unreliability, the greater the spread, and the more time passengers have to budget for waiting. Of course, not all of budgeted waiting time is actually spent waiting on any given day; part is spent waiting, and the remainder is potential waiting time, just as with short-headway service. Like schedule inconvenience, potential waiting time is manifested in passengers arriving earlier than planned at their destination. The difference is that potential waiting time varies from day to day and cannot be counted on in planning daily activities, while schedule adherence is not random, and can be counted on, making it less of a burden to passengers. Using the notation that E[V] equals mean schedule devia- tion, and using the weight of 0.5 suggested earlier for combi- ning potential waiting with platform waiting, summary mea- sures of excess waiting time can be calculated as follows: mean excess platform waiting = E[V] − V0.02 excess budgeted waiting = V0.95 − V0.02 mean potential waiting = V0.95 − E[V] equivalent excess waiting = (excess platform waiting) + 0.5  (potential waiting) = 0.5 (excess platform waiting + excess budgeted waiting) 6.3.2 Example Analyses Example schedule deviation and waiting time summary reports for long-headway service are shown in Figure 16. These figures compare two example cases, each based on 100 synthesized observations: • Case No-OC is a route with relatively poor reliability. Schedule deviation has a standard deviation of 2.2 min, so that only 72% of departures are in an on-time window of 0 to 5 min late. 49 V0.95 = budgeted depature time V0.02 = earliest likely bus dep. time = target arrival time pax arrival V = bus departure time synchronization time excess platform waiting potential waiting time excess budgeted waiting time Figure 15. Long-headway waiting time components. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% a. Distribution of Schedule Deviations case No-OC case OC >10 min late 5+ to 10 min late 3+ to 5 min late On time One minute early > 1 min early 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 case No- OC case OC m in ut es excess budgeted wait equivalent excess wait excess platform wait b. Waiting Time Summary Figure 16. Long-headway schedule deviation and waiting time analysis.

50 Component Case No-OC(min) Case OC (min) Change (min) 2nd-percentile schedule deviation -1.0 0.1 1.1 Mean schedule deviation 3.48 1.88 -1.60 95th-percentile schedule deviation 6.8 4.6 -2.2 Mean excess platform wait 4.5 1.8 -2.7 Equivalent excess wait 6.2 3.2 -3.0 Excess budgeted wait 7.9 4.6 -3.3 Potential wait 3.4 2.8 -0.6 Table 7. Waiting time component comparison. • Case OC is the same route, and has the same underlying variability, as Case No-OC,but operational control is applied by holding, and the scheduled departure time has been shifted earlier by 2.2 min. With that schedule adjustment, the earliest 30% of departures will be held; as a result, they are assumed to have random schedule deviations between 0 and 1.5 min. Figure 16(a) shows a strong improvement in operational quality reflected in the distribution of schedule deviations. The 5% of trips that were early disappear, and the percentage of trips in the 0- to 5-min window rises from 70% to 97%. The percentage of trips in the highest quality category (0 to 3 min late) rises from 39% to 79%. The waiting time summary found in Figure 16(b) expresses these results in terms of impact to passengers. Mean platform waiting time falls by 2.7 min because passengers do not have to arrive before the scheduled departure time and the average schedule deviation has been reduced considerably. Counting changes in potential waiting time, there is net reduction in equivalent waiting time of 3 min. Table 7 provides additional detail on how operational con- trol shrinks the spread between early and late schedule devi- ations. The 2nd-percentile schedule deviation rises by 1.1 min and the 95th-percentile schedule deviation falls by 2.2 min, shrinking excess budgeted waiting time by 3.3 min. Because potential waiting time has most to do with the upper end of the schedule deviation distribution, actions that reduce the upper end (gross lateness) tend to most affect potential waiting time, while actions that reduce the lower end (earliness) tend to reduce platform time, as in the example. Because platform waiting time affects passengers more strongly than potential, actions that reduce earliness are therefore particularly effective. The mean waiting time calculations do not account for the (small) percentage of passengers who miss their bus (perhaps because the bus was early) and have to wait a full headway for the next one. The reason this percentage is not taken into account is two-fold. First, the expected penalty for missing the bus is 0.02 h, where h is the scheduled headway, and 0.02 is the probability of missing the bus. Because this quantity depends on the planned headway rather than on a schedule deviation, it does not contribute to excess waiting time because it will be the same regardless of service reliability. (That would not be the case if the target arrival time were not percentile-based, e.g., if it were set at 1 min before the scheduled departure time, for example.) Second, while the immediate impact of an early bus is to make a few passengers wait a long time, in the long term the impact of early buses is to make all passengers arrive earlier at the bus stop every day. For example, a passenger who misses a bus on a route with a 20-min headway suffers a 20-min waiting time penalty that day. However, for maybe the next 100 days, the passenger will arrive at the stop 2 min earlier to be sure to not miss the bus again, which costs him 200 min- utes of additional waiting. As this simple example shows, the impact of earliness on waiting time is accounted for by setting the target arrival time to the 2nd-percentile schedule devia- tion, which is sensitive to earliness. To reiterate, determining extreme values from data requires large sample sizes. A rule of thumb is that there should be at least 5 observations outside the extreme value estimated. Therefore, about 250 observations are needed to make a reli- able estimate of the 2nd-percentile schedule deviation. AVL will provide that kind of sample size, but it may be necessary to aggregate over a considerable date range and/or over a period of the day with several scheduled trips.