Dynamics of route choice and signal control in capacitated networks

This paper considers the stability of the dynamical system which arises when a responsive control system is utilised in a signal-controlled urban road network. In this case current traffic flows change current green-times (according to the responsive control policy) and current green-times change current delays and hence drivers' route choices and current flows. Simple networks only are considered; starting with a small symmetrical network with two routes and a traffic signal which follows the equisaturation control policy. The symmetrical equilibrium, with equal flows on both routes, is (under reasonable conditions) unstable. The paper then shows that, within the simple network considered, bottlenecks may be added which makes the symmetrical equilibrium stable for certain steady Origin-Destination loads. Finally the paper considers the stability of a similar asymmetrical network when a special responsive policy is used. Under natural conditions the network is shown to be stable under this policy for all feasible Origin-Destination loads. The stability proof given for this network is designed to generalise so as to apply to a general signal-controlled network under suitable conditions; however such a general stability proof is not included in this paper.