Max-pressure signal control with cyclical phase structure

Max-pressure traffic signal control has many desirable properties. It is analytically proven to maximize network throughput if demand could be served by any signal control. Despite its network-level stability properties, the control itself is decentralized and therefore easily computed by individual intersection controllers. Discussions with city engineers have suggested that a major barrier to implementation in practice is the non-cyclical phase actuation of max-pressure control, which can actuate any phase, in arbitrary order, to serve the queue(s) with highest pressure. This arbitrary phase selection may be confusing to travelers expecting a signal cycle, and is therefore unacceptable to some city traffic engineers. This paper revises the original max-pressure control to include a signal cycle constraint. The max-pressure control must actuate an exogenous set of phases in order, with each phase actuated at least one time step per cycle. Each cycle has a maximum length, but the length can be reduced if desired. Within those constraints, we define a modified max-pressure control and prove its maximum stability property. The revised max-pressure control takes the form of a model predictive control with a one cycle lookahead, but we prove that the optimal solution can be easily found by enumerating over phases. The policy is still decentralized. Numerical results show that as expected, the cyclical max-pressure control performs slightly worse than the original max-pressure control due to the additional constraints, but with the advantage of greater palatability for implementation in practice.