A queuing approach to speed-flow relationships on freeways

Abstract

Paper presented at the 23rd Annual Southern African Transport Conference 12 - 15 July 2004 "Getting recognition for the importance of transport", CSIR International Convention Centre, Pretoria, South Africa. Speed-flow relationships have traditionally been used to describe non-interrupted traffic operations on basic freeway segments. Such relationships typically show that when traffic flow is stable, speed reduces as traffic flow increases up to the maximum flow or capacity of the freeway. However, when traffic flow is unstable, the inverse of the above relationships is obtained. In this paper, an innovative approach to the traditional speed-flow relationship is discussed. It is shown that the traffic on freeways can be analysed in terms of travelling queues or platoons. The queue or platoon lengths are dependent on the traffic flow and it is therefore possible to develop queue length - flow relationships. Speeds can be related to the queue length and it is therefore possible to develop speed-queue relationships. The combination of these relationships provides the traditional speed-flow relationship. The advantage of the queuing approach is that it can be used to explain and clarify many of the operational characteristics of freeways. Queues or platoons form because of speed differentials between fast and slow vehicles. Faster vehicles therefore travel at lower speeds in these queues with the result that the average speed of the traffic stream reduces. Long queues create the problem that any disturbances along a freeway typically result in shock waves within the queues and in unstable flow. Various factors can contribute to such unstable flows, such as accidents and other incidents. Mostly, however, unstable flow occurs typically at interchanges where large volumes of traffic enter the freeway or where queues of traffic spill back from the interchange onto the freeway. Unstable flow can also occur on steep upgrades on which climbing lanes have not been provided.