A time-dependent speed - flow model based on queuing theory concepts (referred to as Akçelik's function in the literature) was previously used to develop alternative versions of the HCM speed - flow models for basic freeway segments, multilane highways and urban streets. This paper introduces an explicit model that describes in-stream vehicle interactions and resulting queuing in terms of traffic bunching characteristics. For this purpose, the bunched exponential model of the distribution of vehicle headways is used. A new model of the proportion of bunched vehicles is proposed. The model uses the delay parameter of Akçelik's speed - flow model as a bunching parameter, thus linking the bunching and speed - flow models. The paper also discusses the driver response time parameter at capacity flow. A model for forced flow conditions is then developed, and unsaturated and forced flow conditions are contrasted for the purpose of determining headway distributions. The paper also discusses application of the new bunching model and the associated speed - flow model to roundabout circulating streams.
AKÇELIK, R. (2003). Speed - Flow and Bunching Relationships for Uninterrupted Flows. Paper presented at the 25th Conference of Australian Institutes of Transport Research (CAITR 2003), University of South Australia, Adelaide, Australia, Dec 2003.