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35 Because schedules are written at the timepoint level, time- a representative sample of stops, making it possible, although point data will support schedule adherence analysis. And not ideal, to estimate headway-related measures of opera- because schedule adherence involves estimating proportions tional quality from timepoint data. To the degree that opera- and extremes (detecting the percentage of early and late trips), tors hold at timepoints, however, using them as representative the full fleet should be equipped. Finally, because schedules stops becomes deceptive. sometimes refer to arrival time as well as departure time, a data collection system that captures both is preferred. 4.6.1 Plotting Trajectories Passenger waiting time on routes with long headways is closely related to schedule adherence. Chapter 6 shows how One much-appreciated AVL data analysis tool is a plot of it is possible to determine excess waiting time from the spread successive trajectories on a route, as illustrated in Figure 5. Its between the 2nd-percentile and 95th-percentile schedule format shows observed versus scheduled trajectories for a line- deviation. direction. In the color version of this graph, each bus appears Passengers are particularly interested in whether they can in a different color so that bus-specific trends (e.g., a slow make their connections. Arriving 4 min late is not a problem if driver) can be spotted. This kind of analysis is helpful for the time allowed for the transfer is 5 min, but it could be a big illustrating the dynamics of bunching and overtaking and for problem if the allowed time is only 3 min. However, if the showing where delays begin and how they propagate. How- departing trip is held--again, the convergence of schedule ever, while this tool is helpful for giving the sense of how a planning and operations control--other issues arise. AVL data route operates, it does not yield any numerical results and is is ideal for determining whether specific connections were met. suitable only for analyzing a single day's data at a time. To analyze connection protection an agency must define the particular connections it wishes to protect or at least analyze. 4.6.2 Headway Analysis The researchers found one transit agency using its archived AVL data for this purpose. Integrating control message data, A numerical analysis of headway data applies over multi- which might include requests for holding to help a passenger ple days, for a route-direction and a period of the day with rel- make a connection, would permit a deeper analysis of oper- atively uniform headways. Typical summary results are mean ational control. Incorporating demand data, ideally transfer and coefficient of variation (cv, which is standard deviation volumes, would make the analysis richer still. divided by mean) of headway. On short-headway routes, the Connection protection analysis requires data structures Transit Capacity and Quality of Service Manual (27) assigns and software that create the capacity to perform analyses levels of service for service reliability based on values of head- across routes. way cv. Mean headway can be compared with mean scheduled headway to see whether more or less service than scheduled was operated. In place of headway cv, Eindhoven uses a regu- 4.6 Headway Regularity and larity index, which is the mean value of the absolute headway Short-Headway Waiting deviation divided by mean headway. On routes with short headways, headway regularity is A distribution of headways is an even richer result than important to passengers because of its impact on waiting time mean and cv of headway, allowing analysts to see how often and crowding. It is also important to the service provider headways were very short or very long, using any threshold because crowding tends to slow operations and because much they desire. For its rapid transit routes, the MBTA uses the of operations control is focused on keeping headways regular. percentage of headways greater than 1.5 scheduled headways To measure headways, data has to be captured on succes- as an indicator of service quality. sive trips, making headway analysis particularly sensitive to Analysis procedures have to be careful in dealing with the rate of data recovery, as one lost trip means two lost head- period boundaries. To illustrate, if the morning peak period ways. Analyzing headway when only part of the bus fleet is ends at 9:00, a trip scheduled to pass a timepoint at 8:58 may instrumented poses the logistical challenge of getting all the pass on some days before 9:00 and on other days after 9:00. In buses operating on a route to be instrumented; because of this an analysis of headways in a period ending at 9:00, that trip challenge, Table 4 indicates headway analysis needs 100% of will sometimes be counted and sometimes not, introducing the fleet to be instrumented with AVL. variability into the analysis as an artifact. Headways matter all along the route, not only at time- points; therefore, stop records are best suited to headway 4.6.3 Passenger Waiting Time analysis. (In fact, headways matter most at stops with high boarding rates.) However, because headways at neighboring On short-headway routes, passengers can be assumed to stops are strongly correlated, timepoints can be thought of as arrive at random; therefore, passenger waiting time can be