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77 County, Maryland, and Cincinnati, Ohio are toward the minute early can be treated as being one headway behind top of this group) had a mean speed of 14.8 mph, while the schedule, because passengers arriving near the scheduled de- 91 bus operators in the 1 to 2.5 million boardings category parture time would have to wait for the next bus. Excess wait (Appleton, Wisconsin, and Pueblo, Colorado are toward the time adds to a passenger's overall wait time; it also affects a bottom of this group) had a mean speed of 16.0 mph. In total, passenger's perceived wait time. A common value in the liter- 247 bus agencies out of 468 reporting (53%) are represented ature is that passengers perceive or value wait time approxi- by groups with mean speeds within 1 mph of the median mately twice as much as in-vehicle time; Furth and Muller speed of 15.2 mph; thus, this median value is representative suggest a value of 1.5 and suggest accounting for "potential of most U.S. bus agencies. wait time," an allowance a rider makes to show up earlier for When a baseline travel time rate of 4 minutes/mile (15 mph) service known to be unreliable, with a value of 0.75 of in- was tested against the Portland data, a much better distribution vehicle time [98]. of LOS grades was obtained, with only 30 to 39% of route Excess wait time makes a passenger's trip take longer than segments receiving LOS A grades, depending on whether intended (i.e., the perceived speed or travel time rate for the route-average or segment-specific speeds were used in the trip is slower). However, the effect of excess wait time on the calculation. travel time rate varies depending on the length of the trip: a However, a baseline travel time rate of 4 minutes/mile, when 2-minute excess wait has a bigger proportional effect on a applied to the San Francisco surveys, results in LOS grades that 10-minute trip than a 2-minute wait for a 20- or 30-minute were too low relative to the frequency of service provided. This trip. The difficulty is in determining what an appropriate trip suggests that a different baseline travel time rate may be ap- length should be. propriate for dense urban areas such as San Francisco or down- The recommended solution is to compare the excess wait town Washington, DC. Further testing of the speed elasticity time with the average trip time. The NTD provides information used in the model would also be appropriate. on weekday boardings and passenger miles by mode each year for most transit systems; an average trip length (miles/ boarding) can be computed from these two variables. (This Reliability calculation assumes that trip lengths are consistent throughout One way that the TCQSM measures transit reliability is the day, which may or may not be the case. Passenger miles are through the coefficient of variation of headway deviations--the only available as daily values. Although the NTD allows agen- standard deviation of headway deviations divided by the cies to report boardings in smaller time increments than a day mean scheduled headway. (A headway deviation of a given (e.g., AM peak, midday, etc.), most choose not to.) bus is the actual headway minus the scheduled headway. Dividing the excess wait time (minutes) by the computed When buses arrive exactly on schedule every time, cvh = 0; average trip length (miles) provides the average effect on the when two buses consistently arrive together, cvh = 1.) overall travel time rate (minutes/mile), which can then be Some believe that a better reflection of headway reliability converted to a perceived travel time rate. For example, if the from a passenger point-of-view is given by excess wait time analysis were being performed in Portland, the average week- (e.g., Furth and Miller (previously cited) and Transport for day passenger miles in 2003 were 765,100, while the average London's transit performance standards), which is the aver- weekday boardings were 214,158, resulting in an average trip age additional time a passenger must wait for a bus to arrive length of 3.57 miles. If the average excess wait time was 2 min- because of non-uniform headways. When passengers arrive utes, the additional travel time rate would be (2 / 3.57) = 0.56 randomly at a stop--the case when service is relatively fre- minutes/mile. The perceived additional travel time rate could quent (the TCQSM suggests this occurs at headways of 10 to be up to twice this value, or 1.12 minutes/mile. 12 minutes or less)--the average passenger will wait half a headway for a bus to arrive. When a bus is late, passengers will Effect of Stop Amenities on wait longer than half a headway on average. The difference in Perceived Waiting Time these two times is the excess wait time. For random passenger arrivals, excess wait time is calcu- Research presented in TRL Report 593 suggests that certain lated as half the scheduled headway multiplied by the square stop amenities, including shelters, lighting, and seating, can of the coefficient of variation of headways (or headway devia- reduce perceived journey time by providing a more comfort- tions) [103, 104]. For non-random arrivals (i.e., for longer able waiting environment. Exhibit 84 presents these values, headways, when passengers would be expected to be familiar converted from pence to in-vehicle time, using an in-vehicle with the schedule and arrive a few minutes before the sched- time value of 4.2 pence per minute. uled departure time), excess wait time is the average number Some authors have suggested that real-time displays at bus of minutes that buses are behind schedule. Buses more than a stops showing the number of minutes until the next bus arrival