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