Recent Developments in Dynamic Traffic Modeling with Applicatons on Large Urban Networks

Professor Thanasis Ziliaskopoulos

ABSTRACT

This presentation is concerned with computing traffic patterns on actual large scale urban networks with time varying demand. A System Optimum (SO) Linear Programming formulation and a User Equilibrium (UE) Variational Inequality one are presented that rely on the origin-destination number of vehicles loaded on the network rather than the flow. An efficient Inner Approximation decomposition heuristic is proposed for solving the UE proposed formulation, by decomposing the problem to simple time-dependent shortest path computations. The SO is solved with commercially available solvers and it is particularly convenient for formulating and solving the Network Design Problem under both Deterministic and Stochastic demand.

The introduced models propagate traffic according to sound traffic models instead of problematic travel time-flow relationships. In the UE case the algorithm uses a traffic simulator to maintain feasibility of the solution and to evaluate the path travel times; it is demonstrated that under certain mild assumptions on the path travel time properties, the algorithm can converge to an equilibrium solution. Both approaches are part of a framework called Visual Interactive System for Transport Algorithms (VISTA) that will be briefly demonstrated. Computational experiments on large networks (for the UE case), such as Chicago ’s six-county network, for various applications will be discussed.