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36 Base-file of 2003/04/10: 106 trips scheduled, 96 trips measured (91 %) stop 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 11:11 11:21 11:31 11:30 Tritapt 1.0 (b82) license holder is Peter Knoppers, Technische Universiteit Delft. Copyright © 1997-2006 TU Delft 11:41 11:51 trip MLT [hh:mm] time [hh:mm] 12:00 12:00 12:10 12:20 12:30 12:30 12:40 12:50 13:00 13:00 1 3 5 7 9 11 0 2 4 6 8 10 12 distance [mile] Source: Hermes (Eindhoven), generated by TriTAPT Figure 5. Observed (solid) versus scheduled (dotted) trajectories. determined and analyzed directly from the headway distribu- load relationship using a least-squared fit. Then, using that tion. As an example, transit agencies in both Brussels and slope, Tri-Met normalizes the loads of individual trips to Paris calculate, from headway data, the percentage of passen- what the loads would have been if the headway had been as gers waiting longer than the scheduled headway plus 2 min. scheduled. As part of this project, analyses of passenger waiting time based on headway data were developed (see Chapter 6). 4.7 Demand Analysis The sources of passenger use data are APCs and fare col- 4.6.4 Headway-Load Analysis lection systems. In this report, the only fare records consid- Headway and load have a simultaneous effect on each ered are location-stamped transactions, because analysis of other--longer headways lead to larger loads, and larger loads farebox data at the route level or higher is routine. lead to longer headways. Analyzing headway and load together can lead to interesting insights. 4.7.1 Demand Along a Route By analyzing headway and load together, Tri-Met created a method for determining to what extent an overload is Passenger demand on a route, for a given direction and caused by headway variation, as opposed to demand vari- period of the day, has three dimensions: geographic (i.e., along ability (28). The idea behind this approach is that overloads the route); between scheduled trips (i.e., how is the 7:15 trip caused by headway variation should be "cured" by better different from the 7:30 trip); and between days. Most analysis headway control, while overloads that cannot be simply views aggregate over two dimensions and analyze the remain- explained by headway variation may require a change in ing one; it is also possible to aggregate over only one dimen- scheduled departure times or headways. Tri-Met estimates, sion, showing the other two in the analysis, as the examples for a given route-direction-period, the slope of the headway- will show.
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37 The geographic dimension of demand is shown in a vol- 4.7.2 Demand Across the Day and ume profile or load profile, depending on whether results Scheduling Headway and are expressed in passengers per hour (volume) or passengers Departure Time per trip (load); another view shows ons and offs by stop. By abstracting the geographical dimension using trip sum- One graphical format, developed by Delft University mary measures such as total boardings, maximum load, and researchers and illustrated as the lower step line in Figure 6, passenger-miles, one can focus on the other two dimensions shows not only mean segment loads, but also mean offs, ons, of demand, variation within a day and between days. Figure 7 and through load at each stop in a single profile. The upper, shows how demand varies between scheduled trips, with gray step function indicates 85th-percentile segment loads, scheduled trips on the horizontal axis and one measure of thus adding the dimension of day-to-day variation. This demand, in this case mean boardings, on the vertical. In other report has already pointed out the importance of extreme versions of this graph (not shown), day-to-day variation is values of load for both passenger service quality monitoring presented by showing a scatterplot (horizontal whiskers) or and scheduling. Also shown in Figure 6 for each stop, as well selected percentile values, which allows one to see extreme as for the route as a whole, are box and whiskers plots of offs values of load that are important to both scheduling and (just to the left of each stop) and ons. The box extends from operational control. Using established thresholds, trips can be the 15th percentile to the 85th percentile; a bar indicates the categorized and counted by degree of crowding. mean value; and the X above the box indicates the maxi- In Figure 7, four of the scheduled trips in the period ana- mum observed value. lyzed had no valid APC data. They are represented with a Analysis of demand along a route is necessary for under- large X and a more darkly colored bar whose height is set standing where along the route high loads occur. It supports equal to the average of the nearest trip before and after it with decisions about stop relocation and installing stop amenities, valid counts. The issue of imputing values to missing data is and routing and scheduling actions that affect some parts of discussed in Chapter 11. a route differently from others, such as short turning, zonal Passenger-miles is another summary measure over a route, service, and limited stop service (33). being the product of the segment load multiplied by the Balanced passenger counts (min, mean, 85% and max) Company: HTM Departure times Dates: 2001/11/05 until 2001/11/08 Trips scheduled: 60 (Count) Line: 25 From: Lozerlaan From: 07:00 Mon Tue Wed Thu Fri Sat Sun Total Trips used: 35 (58%) Route: 1 To: Station CS uitstap Until: 09:00 1 1 1 1 0 0 0 4 Trips excluded: 5 ( 8%) 0.3 0.6 2.2 4.1 4.7 6.1 5.6 6.8 7.6 4.1 2.9 6.7 %pmile 0.4 0.8 2.0 5.4 4.1 6.2 4.5 8.9 5.2 7.0 4.0 100 95 90 85 Tritapt 1.0 (b82) license holder is Peter Knoppers, Technische Universiteit Delft. Copyright © 1997-2006 TU Delft 80 75 70 65 60 passengers 55 50 45 40 35 30 25 20 15 10 5 0 EW LL VL DW GL ZP DL HP WZ GM AV SC LL MS BL He LW AP SP SS VP Br SV NH Total stop Source: Delft University, generated by TriTAPT Figure 6. Load and on/off profile.
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38 Balanced unlinked passenger trips per vehicle trip (estimated mean 67.9) Company: HTM Departure times Dates: 2001/11/05 until 2001/11/08 Trips scheduled: 244 (Count) Line: 25 From: Lozerlaan From: 00:00 Mon Tue Wed Thu Fri Sat Sun Total Trips used: 150 (61%) Route: 1 To: Station CS uitstap Until: 15:00 1 1 1 1 0 0 0 4 Trips excluded: 19 ( 8%) Count 2 2 1 1 2 4 4 3 2 3 4 3 0 0 3 0 2 2 0 2 3 3 2 1 4 3 3 3 1 4 3 3 3 4 2 3 2 2 2 4 2 150 145 140 135 130 Tritapt 1.0 (b82) license holder is Peter Knoppers, Technische Universiteit Delft. Copyright © 1997-2006 TU Delft 125 120 115 110 105 100 95 passengers 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 09:00 11:00 13:00 08:00 10:00 12:00 14:00 time [hh:mm] Source: Delft University, generated by TriTAPT Figure 7. Boardings by trip across the day. segment length. When divided by overall route length, this In the future, there may be scheduling tools that account total indicates the average vehicle occupancy along the route. for within-day and between-day variation in demand, as well Special considerations relative to measuring passenger-miles as within-day and between-day variation in running time, in are covered in Chapters 8 and 9. order to design route schedules that respond to how both An analysis of demand variation across the day supports demand and running times vary across the day, using statis- scheduling, which, in part, sets headways and departure times tical methods to limit the probability of overcrowding and so as to achieve target loads. There remains the opportunity insufficient recovery time. to develop design tools for scheduling that take advantage of large APC sample sizes to estimate a demand profile across 4.7.3 Passenger Crowding the day. Using passenger counts combined with measured headways, and averaging over many days, one should be able There is a strong relationship between vehicle crowding to derive the passenger arrival rate as a function of time. and passengers' experience of crowding, but the perspectives Combining these arrival rates in small (e.g., 1-min) time slices are different. For example, if half the trips are empty and half using a reference frame that moves at the speed of a bus allows are overcrowded, then only 50% of the trips are overcrowded, one to predict the peak load on a trip based on its departure yet 100% of the passengers experience an overcrowded trip. time and the departure time of its leader. Measures of crowding from the passenger perspective are dis- With a minute-by-minute load profile across the day, one cussed in Chapter 7. valuable tool would be able to find periods of homogeneous demand within which a constant headway can be used, anal- 4.7.4 Pass-Ups and Special Uses ogous to scheduling tools that seek periods of homogeneous running times. Another valuable tool would not assume con- Operator-initiated incident codes used to register such events stant headways at all, but would select departure times that as pass-ups, wheelchair customers, and bicycle customers can balance loads between trips, accounting for how demand be used to analyze special demands and events along a route rates vary across the day, as suggested by Ceder (34). Tools or across the day. Being able to locate them along a route of this sort are currently under development for the transit might be useful for load analysis, running time analysis, and agency of the Hague. facility planning.