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

OCR for page 46
47 14.00 12.00 budgeted waiting time 10.00 equivalent waiting time actual 8.00 platform waiting time ideal 6.00 (values in minutes, 4.00 represented by cumulative 2.00 heights) 0 2 4 6 8 10 12 14 0.00 waiting time (min) actual actual waiting, waiting, Figure 12. Passenger waiting time distribution for case a case b Example 1. Figure 14. Passenger waiting time comparison for Example 2. 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 ple, for which scheduled headways in the period of interest waiting time equals 10.6 min for the actual headway distribu- are not all equal: tion; for the ideal headway distribution, 95th-percentile wait- ing equals 7.6 min. Example 2 scheduled headways: {5, 8, 8, 8, 8, , 8, 8, 8, 9, 9, 9} minutes 6.2.2 Waiting Time Summary With Example 2, two datasets of 100 observed headways each While the graph of the distribution of waiting time helps are compared: Case a, with high irregularity (headway cv = explain the relationship between headways and waiting time, 0.52), and Case b, with low irregularity (headway cv = 0.26). it is not a useful format for management reporting or service (Actual data values can be found in the spreadsheet file on the quality monitoring. Two other formats are therefore offered. project description web page for TCRP Project H-28 on the The first format for summarizing passengers' waiting time TRB website: www.trb.org.) The waiting time summary in Fig- experience is a summary of platform, budgeted, and equiva- ure 14 shows that, with the reduction in irregularity, mean plat- lent waiting time, as shown in Figure 13. Optionally, the user form waiting falls only a little, from 5.1 to 4.3 min; budgeted can show how waiting time breaks out between ideal and waiting time falls much more, from 12.0 to 9.0 min. Combin- excess waiting time. For example, the 10.6 min of budgeted ing these waiting components under the composite measure waiting time divides into an ideal budgeted waiting time of equivalent waiting time shows that the reduction in irregular- 7.6 min and an excess budgeted waiting time of 3.0 min. Like- ity saves passengers the equivalent of 1.9 min of waiting time-- wise, equivalent waiting time, being 7.6 min, divides into ideal a result that, if service reliability were not accounted for, would and excess parts of 5.8 and 1.8 min, respectively. Therefore, require a headway reduction of almost 4 min, an action that irregularity on this route costs passengers the equivalent of would double operating cost. 1.8 min of waiting time. This example illustrates how the measures budgeted wait- This format can also be used in a beforeafter comparison, ing time and equivalent waiting time reflect the impact of as shown in Figure 14. Figure 14 is based on a different exam- service reliability on passengers. 12.00 6.2.3 Percentage of Passengers 10.00 budgeted waiting time with Excessive Waiting Times 8.00 equivalent waiting time A second useful reporting format shows the percentage of 6.00 passengers in various waiting time ranges or "bins." This for- platform waiting time 4.00 mat can be used to support a service quality standard such as 2.00 (values represented by "no more than 5% of passengers should have to wait longer cumulative heights) 0.00 than (scheduled headway + 2) minutes." In its program for cer- actual ideal excess tifying bus service quality, the French quality institute AFNOR waiting waiting waiting Certification applies a standard in this format (36). Transit Figure 13. Passenger waiting time summary for agencies in Paris, Brussels, and Lyon are among those with at Example 1. least some bus lines certified under this standard.