Novel Speed-Flow Model Based on Queuing Theory and Its Potential Application in Highway Capacity Guidelines

Abstract

Speed-flow relationships are incorporated in many highway capacity guidelines such as the U.S. Highway Capacity Manual (HCM) and the German Highway Capacity Manual (HBS). The speed-flow relationship can be used to predict the operating speed depending on the traffic volume. Based on traffic-flow theory, many models for the speed-flow relationship under fluid and congested traffic conditions have been developed. However, most of the speed-flow relationships used in guidelines are either based on empirical regression analysis and thus lack a theoretical background or include model parameters that do not have a realistic meaning. In this paper, a speed-flow relationship is derived based on the queuing theory in a form that the main model parameters can be expressed as real traffic-flow parameters, which can be obtained by field measurements. These parameters are the free-flow speed, the potential capacity of the imbedded queuing system, and a parameter for the stochastics of the queuing system. By varying the model parameters, different geometric, traffic, and control conditions can be considered. Even the impact of new technologies such as connected and automated vehicles can be accounted for by adjusting those parameters.