Optimizing Network Flows with Congestion-Based Flow Reductions

When optimizing traffic systems using time-expanded network flow models, traffic congestion is an important consideration because it can decrease both the discharge traffic flow rate and speed. One widely used modeling framework is the Cell Transmission Model (CTM) (see Daganzo, Transp Res-B 28(4):269–287, 1994 , Transp Res-B 29(2):79–93, 1995 ), which is implemented in a linear program (LP) in Ziliaskopoulos (Transp Sci 34(1):37–49, 2000 ). While the CTM models the reduction in speed associated with congestion and the backward propagation of congestion, it does not properly model the reduction in discharge flow from a bottleneck after the onset of congestion. This paper discusses this issue and proposes a generalization of the CTM that takes into account this important phenomena. Plainly, an optimization that does not consider this important negative result of congestion can be problematic, e.g., in an evacuation setting such an optimization would assume that congestion does not impact network clearance time, which can result in poor evacuation strategies. In generalizing the CTM, a fairly simple modification is made, yet it can have significant impacts on the results. For instance, we show that for the generalized CTM the traffic holding (a result of the linearization of the CTM flow constraints) plays a more harmful role, which thus requires a scheme to eliminate traffic holding. In this paper, we propose a mixed binary program to eliminate traffic holding, along with methods to improve solvability. Copyright Springer Science+Business Media, LLC 2013