The concept of reserve capacity provides a measure of the performance of a junction, and involves determining the uniform factor by which the existing flows into the junction can be multiplied before any of the approach flows reaches its capacity. Previous work has been limited to cases in which it is assumed there is no "blocking back"- either because the junction is isolated or the queues are assumed to stack vertically. However, in practice, at closely-spaced junctions a queue at one junction may extend and interfere with the operation of an upstream junction, so that some of the available green time at that junction is lost.In this paper the cell transmission model is used to represent the spatial extent of queues in networks with closely-spaced signalised junctions. It is shown that the problem of estimating the reserve capacity can be formulated as an optimisation problem with linear constraints. By exploiting the problem's structure, an efficient solution algorithm is developed, that consists of solving a sequence of small linear programming problems. The application of the algorithm is illustrated by means of a small example network consisting of two closely-spaced signalised junctions. (A) Reprinted with permission from Elsevier. For the covering abstract see ITRD E134766.
Abstract