Quasi-dynamic traffic assignment with spatial queueing, control and blocking back

This paper introduces a steady-state, fixed (or inelastic) demand equilibrium model with explicit link-exit capacities, explicit bottleneck or queueing delays and explicit bounds on queue storage capacities. The model is a quasi-dynamic model. The link model at the heart of this quasi-dynamic equilibrium model is a spatial queueing model, which takes account of the space taken up by queues both when there is no blocking back and also when there is blocking back. The paper shows that if this quasi-dynamic model is utilised then for any feasible demand there is an equilibrium solution, provided (i) queue storage capacities are large or (ii) prices are used to help impose capacity restrictions; the prices either remove queueing delays entirely or just reduce spatial queues sufficiently to ensure that blocking back does not occur at equilibrium. Similar results, but now involving the P0 control policy (introduced in Smith (1979a, 1987)) and two new variations of this policy (i.e., the spatial P0 control policy, and the biased spatial P0 control policy) are obtained. In these results, the control policies allow green-times to vary in response to prices as well as spatial queueing delays. These three policies are also tested on a small simple network. In these tests, the biased spatial version of P0 is much the best in reducing equilibrium delays (on this simple network). The paper further illustrates how the spatial queueing model works on simple networks with different merge models; it is demonstrated that equilibrium may be prevented by certain (fixed ratio) merge models. It is also shown in this case that equilibrium may be imposed on just the controlled area itself by a variety of (merge model, gating strategy) combinations. Opportunities for developing such combined gating and merging control strategies are finally discussed.