MSA Algorithms for solving SUE in Urban Transit Networks

Abstract

This paper addresses the Stochastic User Equilibrium assignment with mixed pre-trip en-route path choice behavior. This problem is relevant for urban transit networks: when travelers begin their journey they may not completely know the status of service, say bus arrivals at stops, and may only choose a travelling strategy at origin. Under mild assumptions such strategies can be modelled as hyperpaths, thus user choice behavior can be modelled through Random Utility Models applied to the set of (elementary) hyperpaths, such as Probit and Gammit; these models allow for general co-variance matrices but their application requires Montecarlo techniques. Several MSA-based algorithms have been presented and compared on a simple network using both Mersenne Twister pseudo-random numbers and Sobol quasi-random numbers.