Backpressure or no backpressure? Two simple examples

Many responsive traffic signal control strategies are “pressure-driven”. These strategies move green-time from stages with a lower pressure to stages with a higher pressure, at each junction; often aiming to approximately equalise stage pressures at each junction. In some of these pressure-driven strategies each stage pressure at a junction includes a “backpressure” term, which depends on downstream links. Such backpressure terms reduce the pressure on stages and reduce pressure most for those stages leading toward the most highly congested downstream road links. The expectation is that there will then be a reduction in traffic flow exiting the junction toward already highly congested road links, and that this will reduce queue lengths and network delays. This paper shows that this is not always the case by giving two examples where having backpressure within the control policy on a network with two signal controlled junctions

(1) increases both equilibrium delays at one of the junctions for certain demands, and

(2) never reduces any of the equilibrium delays at either junction.

A simple dynamic evolution with a steady reduction in demand is also shown in which two of the considered policies, one with backpressure, give rise to equilibrium delays and queues which tend to infinity, and reveal a gap; in this gap feasible demands have no equilibrium consistent with the two control policies and in a day-to-day dynamical context delays and queues are unbounded. This paper considers only the simple network shown in figure 1 under certain specified conditions. One main avenue for further research might be to consider whether the results shown here also hold in different networks under different conditions.