Zero-queue traffic control, using green-times and prices together

Reducing stationary or very slowly moving queues is one way of reducing congestion, pollution, inefficient stop–start travel and carbon emissions in cities. This paper considers traffic signal control and road pricing together; aiming to eliminate queueing in at least a subnetwork. Link-exit green-times and link-exit bottleneck delays are considered first in some detail; largely using a simple network. The paper then shows that policy P0, specified in Smith (1980, 2015), is capacity-maximising for a general network with vertical queueing delays. Then link exit prices, co-ordinated with green-times and also red times, are considered. It is shown that using prices (instead of delays) in the P0 control policy maximises the capacity of a general steady state network, with zero queues. This steady state capacity-maximisation ＋ zero-queue result is then extended to dynamic networks in two ways; an equilibrium extension and a day-to-day stability extension. The equilibrium extension shows that P0-with-prices maximises network capacity with zero queues in a dynamic network and the stability extension shows that a smoothed version of the P0-with-prices policy, called P0f, is able to deliver some stability as well as zero queue capacity maximisation. A simple example network has been given to illustrate several of the control-with-prices policies. It is shown that a biased version of P0-with-prices, Ph-with-prices, yields, for this simple network, higher utility than P0-with-prices itself.