Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem

Abstract

Two continuous time formulations of the dynamic traffic assignment problem are considered, one that corresponds to system optimization and the other to a version of user optimization on a single mode network using optimal control theory. Pontryagin's necessary conditions are analyzed and given economic interpretations that correspond to intuitive notions regarding dynamic system optimized and dynamic user optimized traffic flow patterns. Notably, we offer the first dynamic generalization of Beckmann's equivalent optimization problem for static user optimized traffic assignment in the form of an optimal control problem. The analysis further establishes that a constraint qualification and convexity requirements for the Hamiltonian, which together ensure that the necessary conditions are also sufficient, are satisfied under commonly encountered regularity conditions.

Autonomous Mobility-on-Demand Systems for Future Urban Mobility

“…A remarkable feature of these approaches is that they yield formal performance bounds for the control policies (i.e., factor of sub-optimality) and scaling laws for the quality of service in terms of model data, which can provide useful guidelines for selecting system parameters (e.g., number of vehicles). These approaches take their origin from seminal works on hypercube models for spatial queues [19], on the Dynamic Traveling Repairman problem [20,21,22,23], and on the Dynamic Traffic Assignment problem [24,25].…”

The modelling of dynamic route guidance systems

“…We mention finally in passing that the need to represent the effect of time-varying demand and queuing has already prompted a great deal of effort in developing a dynamic extension of Wardrop's equilibrium (for example : Friesz et al, 1989;Smith & Ghali, 1990;Janson, 1991;Papageorgiou, 1991). At present the problem is unsolved for general transportation networks; indeed, there is not even a consensus over what the dynamic extension should be.…”

An improved routing algorithm using chaotic neurodynamics for packet routing problems

“…Typical examples of static combinatorial optimization problems are the traveling salesman problem [1,2], the quadratic assignment problem [3] and the vehicle routing problem [4], whereas examples of dynamic combinatorial optimization problems are the packet routing problem [5][6][7][8][9][10][11][12][13][14][15][16][17] and the traffic flow control problem [18]. In static combinatorial optimization problems, the search space of the solution does not change.…”