Modelling network flow with and without link interactions: the cases of point queue, spatial queue and cell transmission model

Abstract

This paper studies dynamic network models in which congestion takes the form of queuing behind bottlenecks. The three models in consideration, the point queue (P-Q) model, the spatial queue (S-Q) model and the cell transmission model, all deal with queues caused by temporal bottlenecks, yet differ with each other in describing the S-Q characteristics. Our work focuses on exploring the impacts of spatial distribution of queues on the result of dynamic network loading (DNL). For this purpose, simple node models (merge and diverge) are introduced to describe flow interactions across links. We present a numerical solution algorithm to the DNL problem which accommodates the three models in a general framework. Analytical solutions are derived for simple cases and agree with numerical results. Our limited experiments indicate that P-Q and S-Q may severely underestimate network travel costs under DNL, particularly when queue spillback prevails.