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75 When summary records are created, it is still important to erally provided in a stop list for each pattern (sometimes preserve the possibility of drilling down to original records called "branch" or "variation"). A trip that deviates by even a that have not been aggregated. single stop must be classified as a separate pattern. Profiles can readily be aggregated over scheduled trips fol- lowing the same pattern. Aggregating this kind of report over 11.4.2 Accounting for Varying Sample Size completely different patterns is meaningless. However, a cer- The number of days each scheduled trip is observed in a tain pattern that falls between "same" pattern and "completely given date range can vary because of imperfect data recovery, different" pattern presents an analysis challenge. Many tran- especially if data collection uses a rotating instrumented sub- sit systems have route structures in which a line consists fleet. Analyses should account for these varying sample sizes of multiple patterns (cases of up to 20 patterns have been by aggregating in a way that gives every scheduled trip, not observed) that share a common trunk. When several patterns every observation, equal weight. share a common trunk, analysts might be interested in the For example, an easy but incorrect way to determine on- load profile over the trunk, in an analysis of headways along time performance for a line over a date range is to query all the trunk, or in an analysis of running times or delays for all the timepoint records that qualify, and simply get a total of patterns along the trunk. the number with early, on-time, and late departures. How- In the survey of practice, the only shared-trunk analysis ever, if some trips were observed more than others, such an capability seen was for running time, in which running time estimate will be biased in favor of the trips with higher sam- was analyzed for all trips making a selected sequence of time- pling rates. The proper estimation method would be, first, to points. Methods to analyze headways and load profiles on a get an average number of early, on-time, and late departures trunk were either non-existent or ad hoc (i.e., applicable only for each scheduled trip by aggregating over observed days to the particular trunk for which they were developed). and, then, to sum over all the scheduled trips that qualify. As part of this project, a data structure for trunks was If the sample size is so small that some scheduled trips were developed and tested in the TriTAPT environment. Users can not observed, an alternative aggregation scheme is to aggregate define a "virtual route" consisting of a sequence of stops that over observed days within short periods (e.g., 1-hour periods), may be shared, entirely or in part, by multiple route patterns. then expand each period's result according to the number of Users specify the patterns that contribute to the virtual route, scheduled trips in that period, and aggregate over trips. specifying at which stop those patterns enter and leave the vir- tual route. A pattern may enter and leave a virtual route more than once. That way patterns that deviate from a main route 11.4.3 Accounting for Missing Data (e.g., to serve a school or senior housing development for a Two approaches may be taken to deal with trips that were not few trips each day) can be accommodated. Load, schedule observed on a given day. The classic approach is to omit them adherence, headway irregularity, and delay profiles along the from the dataset and to give analysis algorithms appropriate virtual route will then reflect all the trips on the trunk, includ- methods to deal with missing data and account for the vary- ing patterns that branch off it or take detours. ing sampling rates that result, as discussed previously. The virtual route pattern is stored as a permanent data An alternative approach is to place imputed values into the structure, and any analysis that can be performed on a single database whenever data is missing. Imputed values may be route can be performed as well on the virtual route; in the lat- based on historical averages or on values from "similar" trips. ter case, all trips belonging to route patterns that contribute That approach allows analysis algorithms to not have to deal to the virtual route are queried for the analysis. Load profiles with missing data or varying sampling rates. However, sup- made for virtual routes have to account for passengers already plying imputed values is a controversial practice that, to the on board when a trip enters the trunk. researchers' knowledge, has not been done with AVL-APC databases. 11.6 Modularity and Standard Database Formats 11.5 Data Structures for Analysis As mentioned earlier in this chapter, analysis software devel- of Shared-Route Trunks oped by a third party offers modularity and the possibility for Analyses in which stop sequence plays a role are generally analyzing AVL-APC data without developing one's own soft- called "profiles," showing results along the route. Examples ware. However, using third-party software requires using a are load profiles, running time profiles, delay profiles, and standard data structure, which may in turn demand routines to profiles of schedule deviation and headway irregularity. Cre- convert data from its native format. That approach is working ating a profile requires an unambiguous stop sequence, gen- in practice for the transit agencies in Eindhoven and the Hague

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76 that use TriTAPT and for transit agencies in both North Amer- In principle, agencies should be able to use a third party's ica and Europe that use running time analysis tools provided analysis routine yet customize the reporting format. Besides by scheduling software vendors. cosmetic changes (e.g., inserting a logo), agencies might wish As part of this project, the ability to interface archived AVL- to make substantial changes in how results are formatted. APC data from North American transit systems to the Tri- This desire can be accommodated by having analysis rou- TAPT data format was tested. Conversion routines were tines export their results as simple tables, which agencies can developed successfully for three U.S. transit agencies and one then import and format as they wish, perhaps using report- Canadian transit agency, all having different native data for- writing software. For example, all of TriTAPT's analyses, in mats. The Delft University of Technology has made TriTAPT addition to generating a standard graphical report format, conversion routines publicly available, allowing agencies to also generate a table containing all of the numeric results that select one that starts with a database similar to theirs and can be readily exported to a database, spreadsheet, or other modify the program as necessary. platform for formatting as the agency desires.