Access control on networks with unique origin-destination paths

This paper presents improved time-dependent control strategies for small fr eeway 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 t o the system so as to maintain bottleneck flows strictly below capacity, It is also assumed that the time-dependent origin-destination table and the t ime-dependent bottleneck capacities are known, although not always a priori . The proposed control strategies attempt to minimize the total delay (incl uding both system delay and access delay) while avoiding queues inside the system. The problem is formulated as a constrained calculus of variations e xercise that can be cast in the conventional form of optimal control theory and can also be discretized as a mathematical program. Although the first- in-first-out (FIFO) requirement for the access queues introduces undesirabl e non-linearities, exact solutions for four important special cases can be obtained easily. More specifically, for networks with (1) a single origin o r (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 s ingle destination the non-linearities disappear and the problem becomes a l arge-scale linear program. This is also true for general networks if (4) th e fractional distribution of flow across destinations for every origin is i ndependent of time. A greedy heuristic algorithm is proposed for the genera l case. It has been programmed for a personal computer running Windows. The algorithm is non-anticipative in that it regulates access at the current t ime without using future information. As a result, it is computationally ef ficient 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. Significant improvements will likely require an ticipatory information. An illustrative example is given. (C) 2000 Elsevier Science Ltd. All rights reserved.