Solving stochastic assignment to transportation networks with TVs and AVs

This paper focuses on solving stochastic assignment with several types of vehicles, for instance advanced and traditional vehicles, competing for the same arcs and jointly participating to congestion. In urban transportation networks paths likely overlap, thus two path choice models, derived from Random Utility Theory, are analyzed: Probit and Gammit, properly modeling path overlap through covariance between path perceived utilities. Since for these two models no closed form is available for choice probabilities, two specifications of Montecarlo algorithms for assignment to uncongested networks are presented: the efficiency of the commonly used Mersenne Twister Pseudo-Random Number Generator is compared with a PRNG based on Sobol (quasi-random) numbers. Then, several MSA-based algorithms for equilibrium assignment ot congested networks are analyzed: some step size strategies are proposed and compared with existing ones aiming at improving practical rate of convergence. Sufficient convergence conditions are presented for equilibrium assignment with arc cost flow functions with symmetric or asymmetric Jacobian matrix. Results of applications are also discussed to support theoretical results.