Traffic Equilibria and Its Solution in Congested Road Networks

Abstract

The traffic equilibria on a network with congested flows is dealt by considering queues at intersections. The travel time on a link with congested flow is expressed by the sum of the travel time in non-congested flow regime and the imaginary waiting time at the end of the link. Then the traffic equilibria are formulated by adding capacity restraints explicitly to the usual equilibrium traffic assignment problem. The Lagrange multiplier associated with a capacity restraint is equivalent to the waiting time of the link. The solution of the problem provides equilibrium flows with waiting times on congested links. Two solution methods of the problem are proposed. One is the application of Lagrange multiplier method, and the other is the application of interior penalty function method. In view of the computational results, the former is accurate. On the contrary, the latter is approximate but more practical for large scale networks.