THE EFFECT OF QUEUEING ON TRAFFIC ASSIGNMENT IN A SIMPLE ROAD NETWORK

Abstract

A simple road network consists of two nodes connected by two routes, one of which is a high speed road with characteristics typical of urban freeways. A queue forms upstream of a bottleneck on this route when traffic demand exceeds the bottleneck capacity. The second route -- a city street, or set of parallel city streets -- does not allow high speeds, but is uncongested at the traffic levels considered. Two different traffic loading patterns are studied. In the first case the times at which travellers begin their journeys home from work are known. In the second case, the times at which travellers going from home to work must arrive at work are known rather than the time at which they leave home. In both cases it is assumed that the traffic pattern exhibits strong peaking characteristics, with maximum demand in excess of the bottleneck capacity. Deterministic queueing models are used to determine the traffic assignment for each of the two cases under the assumption that each traveller acts in such a way as to minimize his own time losses. In both cases all traffic uses the freeway type route until the queue has grown to such a length that the travel time is equal on the two routes, then the queue length remains constant throughout some time interval during which both routes are in use. When the same curve is used for the traffic demand pattern in the two cases, however, the assignments differ. The queue forms earlier, grows faster, and vanishes earlier in the case where the travellers must reach work on time. Furthermore, the total number of travellers using the second route is not the same in the two cases. The traffic assignment which minimizes total travel time is also determined for each of the two cases. /TRRL/

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