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43 suggested that lies within 2 min of the 85th-percentile makers the power to combine design with analysis. As men- observed running time for (almost) every trip in that period. tioned earlier, the algorithms that suggest homogeneous peri- ods and running times are "compromisers," not "optimizers." These algorithms include various rules for expanding, com- They follow reasonable, systematic rules for determining run- bining, and splitting periods. Other running time analysis pro- ning times, but given that any solution is an imperfect com- grams have similar heuristic algorithms. To the researcher's promise, users may be able to find solutions they prefer. For knowledge, there is no "optimal" formulation for the design example, these algorithms do not consider whether adding a of running times and running time periods. minute of running time might require an extra bus, nor do they consider the burden on passengers of changing the pub- lished schedule. Schedule makers can bring this kind of knowl- 5.1.3 "What-If" Experimentation with Period edge into the design process; they therefore need the flexibility Boundaries and Allowed Times to modify suggested running times and have the program This tool allows users to modify both period boundaries analyze what will happen. and allowed times. The starting point for experimentation can be either the current schedule or the running time peri- 5.2 Determining Running Time ods and allowed times suggested by the program (based on Profiles Using the Passing user-selected parameters). Graphical tools allow the user to Moments Method simply drag period boundaries right or left, split a period, com- bine periods, and drag proposed allowed times up or down; in Once running times for a given route (or route segment) response to any change, the program recalculates each period's and period of the day are selected, the next step is to divide the running time feasibility. Figure 10 shows a user-created set of chosen route (or segment) time by (smaller) segments, creat- running time periods and running times and the resulting ing a scheduled running time profile (cumulative allowed time feasibilities for the same dataset as the previous two figures. from the start of the line). This step must be performed sepa- Having a program automatically suggest new periods and rately for each running time period. For example, take the allowed times based on user-supplied parameters, while also period 8:06 to 8:42, for which the selected allowed time in Fig- allowing schedule makers to experiment with and propose ure 10 was 64 minutes. In the graph shown in Figure 11, the their own set of periods and running times, gives schedule suggested running time profile is shown as the heavy line with Suggested periods based on observed net route section times (feasibility range 50% - 80%) Company: TUD Departure times Dates: 2004/02/17 until 2004/09/10 Trips scheduled: 750 (Calc) Line: 1 From: Stop 1 From: 07:00 Mon Tue Wed Thu Fri Sat Sun Total Trips used: 568 (76%) Route: 1 To: Stop 44 Until: 20:00 2 2 2 2 2 0 0 10 Trips excluded: 36 ( 5%) 8 8 7 8 8 9 7 8 9 9 9 5 8 9 8 8 9 8 6 9 8 9 6 9 6 6 9 9 9 8 8 8 6 8 4 4 7 6 Count 7 7 8 8 7 8 7 6 7 9 5 7 7 9 9 6 7 8 8 8 8 8 6 8 7 8 9 9 8 7 6 8 6 7 8 8 9 75 Tritapt 1.0 (b82) license holder is Peter Knoppers, Technische Universiteit Delft. Copyright 1997-2006 TU Delft route section time [m] 60 45 30 15 61.3% 63.2% 69.6% 60.2% 66.6% 59.1% 65.4%65.1% 61.9% 64.5% 0 08:00 10:00 12:00 14:00 16:00 18:00 20:00 07:00 09:00 11:00 13:00 15:00 17:00 19:00 time [hh:mm] Figure 10. Analysis of user-proposed running times and periods.

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44 Passing moments (Attainability = 69.7%, net time = 64:00) Company: TUD Departure times Dates: 2004/02/17 until 2004/09/10 Trips scheduled: 40 (Calc) Line: 1 From: Stop 1 From: 08:06 Mon Tue Wed Thu Fri Sat Sun Total Trips used: 31 (78%) Route: 1 To: Stop 44 Until: 08:42 2 2 2 2 2 0 0 10 Trips excluded: 1 ( 3%) 00:00 03:04 05:22 07:36 09:36 11:39 14:45 18:34 20:28 24:38 26:53 29:54 32:54 34:35 38:20 40:45 42:34 44:48 47:52 50:04 52:40 57:10 Time 01:48 04:02 06:38 08:47 10:33 13:38 15:58 19:46 22:49 25:55 28:32 31:11 33:58 35:57 39:21 41:33 43:37 46:30 49:01 51:17 54:14 64:00 0 Tritapt 1.0 (b82) license holder is Peter Knoppers, Technische Universiteit Delft. Copyright 1997-2006 TU Delft 15 route section time [m] 30 45 60 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 stop Figure 11. Segment running times or Passing Moment. asterisks at each stop. To show the relation of the suggested from each timepoint to the end of the line is set equal to the running time profile to observed running time data, this for- 70th-percentile completion time from that timepoint. If run- mat includes a light line for every observed running time in ning time data is available at the stop level, a data-driven, the selected period, anchored to a start at time 0. stop-level running time profile will be created, which can be The suggested running time profile uses Muller's Passing valuable for passenger information, operational control, and Moments method, setting the running time from a timepoint traffic signal priority. to the end of the line equal to the f-percentile completion time Running time periods and running times accepted in the from that timepoint, where f is the feasibility (or attainabil- homogeneous periods analysis are stored in memory and listed ity) of the overall route time. For example, in Figure 11 the in a menu, so that users can choose them one at a time to cre- overall route time has 70% feasibility, and so running time ate running time profiles using the Passing Moments tool.