A Dynamic Space-Time Network Flow Model for City Traffic Congestion

A space-time network is used to model traffic flows over time for a capacitated road transportation system having one-way and two-way streets. Also, for the first time, traffic signal lights which change the network structure are explicitly incorporated into the model. A linear (time) cost per unit flow is associated with each arc, and it is shown that under the model structure, travel time on a street is a piecewise linear convex function of the number of units traveling on that street. Hence congestion effects are explicitly considered while maintaining the linear nature of the model. Two efficient solution methods are proposed. A network flow solution for a multiple source single destination network and a shortest path solution for a single source single destination network. Two examples are presented. The first example has one source and one sink. There is a unimodal buildup of traffic at the source (say a factory) which enters the street network as quickly as its capacity permits and proceeds through the network, stopping at red lights when necessary, towards the sink (a residential area). Computations with this example show that the arrival rate has multiple peaks which are induced by the stop lights. In the second example there are multiple sources and one sink. The results here are similar except that the arrival rate has a single broad peak which is due to the extreme symmetry of the constraints of the problem.