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41 CHAPTER 5 Tools for Scheduling Running Time This chapter describes running time analysis and scheduling centile values (jagged lines, set for this figure at 50th and 80th tools that were developed and/or improved as part of this proj- percentile), and maximum observed running time (arrow); ect. They use statistical methods to create running time sched- Current running time periods, bounded by heavy vertical ules, taking advantage of the large sample sizes afforded by AVL lines, with a similar heavy horizontal line indicating current data, and are part of TriTAPT software developed by researchers allowed time; and at the Delft University of Technology. The primary tools Suggested allowed times (thick, gray horizontal lines), about described in this chapter are packaged as two integrated analy- which more will be said later. ses: the first divides the day into running time periods and establishes route running times for each period, and the sec- At the bottom of the rectangle for each running time period ond allocates running time over a route's segments. If the cap- is a calculated value called feasibility; it represents the percent- tured data allows the identification of control (holding) time, age of observed trips in the running time period whose run- these running time tools will be applied to the net running ning time was less than or equal to the current allowed time. time, which excludes control time. Both analyses use graphical reports or screens, behind which 5.1.2 Suggesting New Running Times are exportable tables generated from AVL data. They apply to a and Running Time Periods single route-direction, using data from any number of days. In the graph shown in Figure 9, a set of allowed times and running time periods suggested automatically by the program 5.1 Running Time Periods and are shown and analyzed. A feasibility value is shown for each Scheduled Running Time suggested period. Current allowed times are also visible in the The first analysis, called "homogeneous periods," is a semi- background as solid horizontal line segments. automated, interactive tool for establishing running time The algorithm that suggests running time periods and periods (periods of constant scheduled running time) and allowed times seeks a compromise between trying to closely scheduled running times. This tool allows the user to exam- match the data and having periods as long as possible in order ine the feasibility of the current set of scheduled running to make scheduling and control simpler. TriTAPT offers users times or a user-proposed set of running times, and it also sug- two algorithms for selecting homogeneous periods: gests running times and periods automatically. For one algorithm, users set two percentile limits, for exam- ple, 50% and 80% (the values used in this section's figures). 5.1.1 Feasibility of the Current Timetable The algorithm then seeks periods for which a whole- Figure 8 shows an analysis of the current running times (ver- minute running time can be suggested that lies between the tical axis) and running time periods across the day (horizontal 50th-percentile and 80th-percentile observed running time axis). Features include for (almost) every trip in that period. For the second algorithm, users specify a single feasibility A statistical summary of observed running time for each value and a tolerancefor example, 85% and 2 min. Then, scheduled trip, showing mean (gray bar height), two per- the algorithm seeks periods for which a running time can be

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42 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 Tritapt 1.0 (b82) license holder is Peter Knoppers, Technische Universiteit Delft. Copyright 1997-2006 TU Delft 75 route section time [m] 60 45 30 15 31.0% 31.9% 48.7% 48.9% 40.6% 47.2% 18.5% 45.5% 42.2% 44.6% 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 8. Analysis of current running times. 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 Tritapt 1.0 (b82) license holder is Peter Knoppers, Technische Universiteit Delft. Copyright 1997-2006 TU Delft 75 route section time [m] 60 45 30 15 58.8% 73.7% 66.6% 75.2% 65.4%65.1% 69.1% 58.4% 0 55.8% 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 9. Analysis of automatically suggested running times and periods.