Access Control on Networks with Unique Origin-Destination Paths

This paper presents improved time-dependent control strategies for small freeway networks with bottlenecks and unique origin-destination paths. It is assumed that there are no spill-overs from any of the freeway exits so that freeway queues and delays can be completely avoided by regulating access to the system so as to maintain bottleneck °ows strictly below capacity. It is also assumed that the time-dependent origin-destination table and the time-dependent bottleneck capacities are known, although not always a priori. The proposed control strategies attempt to minimize the ¤This work was supported under a research grant from California PATH total delay (including both system delay and access delay) while avoiding queues inside the system. The problem is formulated as a constrained calculus of variations exercise that can be cast in the conventional form of optimal control theory, and can also be discretized as a mathematical program. Although the ̄rst-in̄rst-out requirement for the access queues introduces undesirable nonlinearities, exact solutions for four important special cases can be obtained easily. More speci ̄cally, for networks with (1) a single origin or (2) a single bottleneck, a myopic strategy which requires the solution of a sequence of simple linear programs is optimal. For networks with (3) a single destination the nonlinearities disappear and the problem becomes a large-scale linear program. This is also true for general networks if (4) the fractional distribution of °ow across destinations for every origin is independent of time. A greedy heuristic algorithm is proposed for the general case. It has been programmed for a personal computer running Windows. The algorithm is non-anticipative in that it regulates access at the current time without using future information. As a result, it is computationally e±cient and can be bolstered with dynamically-updated information. Globally optimal for cases (1) and (2), the heuristic has been developed with slow-varying O-D tables in mind. Signi ̄cant improvements will likely require anticipatory information. An illustrative example is given.