Traffic equilibrium with responsive traffic control

This paper presents a theory of traffic equilibrium which involves responsive signal control policies; in this theory drivers’ route choices and the control policy’s choice of green times are treated in a symmetrical manner. The central theme of the paper is the iterative optimization assignment algorithm. This algorithm may be considered as a means of calculating equilibria which are consistent with a given responsive control policy. But it may also be regarded as a highly idealized model of the day to day dynamics of drivers’ route choices when a responsive signal setting policy is employed; on ‘day’ 1 the signals are held fixed and drivers settle down to an equilibrium flow pattern, on ‘day 2’ the flow pattern is held fixed and the signals are updated according to the control policy for the fixed flow pattern, on ‘day’ 3 the signals are held fixed and drivers settle down to an equilibrium flow pattern.... The authors state natural but strong conditions on the responsive control policy which guarantee that this algorithm is bound to converge to a convex set of (flow, control) pairs such that (i) the flow is a user equilibrium and (ii) the control parameters satisfy the responsive control policy; and they give a proof of convergence under these conditions-the authors do not seek to minimize total travel cost. The present conditions involve the delay or cost formula used; with the BPR cost formula, modified in a natural way to allow for green times, the traditional policy of choosing control parameters which minimize delay for the observed traffic pattern does satisfy these conditions in full. However, with Webster’s delay formula traditional control policies are a long way from satisfying the conditions; and seeking to satisfy them with this delay formula leads the authors to two novel control policies. They assume throughout that demand is determined by a fixed OD matrix, giving the steady total flow rates for each OD pair. The authors also suppose that network characteristics do not change; so that incidents are not considered and saturation flows, for example, are constant.