RECURSIVE STRUCTURE FOR EXACT LINE PROBABILITIES AND EXPECTED WAITING TIMES IN MULTIPATH TRANSIT ASSIGNMENT

Abstract

Exact analytical expressions for incorporation into transit network assignment frameworks are presented. These expressions apply to the case of random uniform passenger arrivals and fixed constant line headways. Previously, difficulty in specification has led to assumptions such as Poisson line arrivals; the reality, however, conforms more to fixed schedules than to Poisson line arrivals. The exact expressions that are derived define expected waiting times and line ridership probabilities. Recursive schemes are developed for computational implementation of these expressions by which to facilitate their application in practical transit assignment. The expressions were developed for multipath assignment schemes and can be used to enhance existing transit assignment algorithms in commonly used planning packages; applications can be either in the line enumeration phase or in the line ridership probability calculations. Numerical examples are provided to illustrate the application of the recursive schemes, and the predicted line probabilities are compared with simulated passenger and line arrivals.

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