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…. We 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 we give a proof of convergence under these conditions—we do not seek to minimize total travel cost. Our 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 our conditions; and seeking to satisfy them with this delay formula leads us to two novel control policies. We assume throughout that demand is determined by a fixed OD matrix, giving the steady total flow rates for each OD pair. We also suppose that network characteristics do not change; so that incidents are not considered and saturation flows, for example, are constant.

In attempting to simulate the operation of a dynamic route guidance system, the modelling task is concerned both with the operation of the control system and with the implications this has for modelling driver hehaviour (whether or not the driver is receiving information from the controller) and network conditions. The aim of this paper is to provide an overview of the modelling issues which need to be considered when addressing such a problem, and which have been identified by various authors in reports on experimentallsurvey work and in discussion papers.In discussing the great number of challenges to the modelling world which have arisen from the interest in such systems, we seek to stimulate further discussion and to provide a framework within which any route guidance model may be critically evaluated. We consider such a framework to be particularly timely in the light of the wealth of simulation models currently being proposedand widely varying conclusions being drawn -as a result of many major research initiatives currently underway throughout the developed world.It is our belief that the development of a model which adequately represents the performance of a dynamic route guidance system is of the utmost importance to the success of such an approach.It will not only provide a means for evaluating the potential benefits, but should also provide an essential insight into the most appropriate means for its implementation and improve our understanding of transportation networks.

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