MINIMIZING DELAYS FOR TRANSIENT DEMANDS WITH APPLICATION TO SIGNALIZED ROAD JUNCTIONS

Abstract Queuing systems such as signalized road intersections have been commonly treated as time-stationary stochastic processes for estimating factors such as delay. Stationary stochastic processes have characteristics delay functions which go asymptotically to infinity as demand approaches capacity. Many queuing processes are non-stationary, having periodic finite queues which are generally dissipated in a finite amount of time, and should not be treated as being stationary. Vehicle arrivals at a roadway section generally constitute a time-dependent process, especially during the critical peak periods. The delay for such a process can usually be approximated reasonably accurately by a simple deterministic transient analysis with perhaps some correction to account for randomness. For an example of the treatment of transient demands, specific attention is given to delay at an intersection, where the demands on the various approaches are time-dependent but assumed time-stationary over short time slices. A procedure is outlined for minimizing the total delay at an intersection over a time period during which the expected approach flows may vary and there may be queuing. The procedure has provision for any short-term queuing inherent in a global optimal solution, and for varying the green split as the demands vary. The delay at each approach is a function of its time-dependent allocation of green time, where the green time reflects its capacity in a given time slice. This procedure differs from the conventional one by relating delay to capacity for given flow instead of relating delay to flow for given capacity.