Abstract 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 $P_0$, 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 $P_0$ 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 $P_0$-with-prices maximises network capacity with zero queues in a dynamic network and the stability extension shows that a smoothed version of the $P_0$-with-prices policy, called $P_0^f$, 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 $P_0$-with-prices, $P_h$-with-prices, yields, for this simple network, higher utility than $P_0$-with-prices itself.

Highlights • $P_0$ signal control with prices maximises network capacity at equilibrium with zero queues. • This result is shown initially for certain steady state networks. • The zero-queue + max-capacity, equilibrium, result is shown to hold in a dynamic model. • Under certain conditions, a special zero-queue + max-capacity policy is stable in a dynamic model.