Urban transportation networks : analytical modeling of spatial dependencies and calibration techniques for stochastic traffic simulators

Abstract

Exact numerical evaluation of the stationary joint queue-length distribution of a Markovian finite capacity network with arbitrary size and topology can be obtained numerically. Nonetheless, the main challenge to such an approach remains the dimensionality of the joint distribution, which is exponential in the number of queues. This thesis proposes an analytical approximation of the joint distribution with a dimension that is linear in the number of queues. The method decomposes the network into overlapping subnetworks. The state of each subnetwork is described aggregately, i.e. in terms of a reduced state space, while ensuring consistency with the disaggregate, i.e., full state space, distribution. This aggregation-disaggregation technique is proposed for the analysis of Markovian tandem finite capacity queueing networks. The model is validated. We present its use to address an urban traffic control problem, and show the added value of accounting for higher-order spatial between-queue dependency information in the control of congested networks. A second, distinct goal of this thesis is to examine the calibration of route choice parameters in microscopic traffic simulators. Automatically calibrating simulators using traffic counts requires describing the relationship between route choice and traffic flows. This thesis proposes an analytical finite capacity queueing model that accounts for the relationship between route choice and traffic flows. The method is embedded in a simulation-based optimization framework and applied to a calibration problem.