Computing Individual Path Marginal Cost in Networks with Queue Spillbacks

“Individual path marginal cost” (IPMC) is defined as the change in travel cost of one unit of flow on a time-dependent path caused by one unit of flow on another time-dependent path. Knowledge of IPMC is central to dynamic transportation modeling, for instance, to compute system-optimal network performance, to solve a dynamic origin–destination (O-D) estimation problem, and to analyze equity issues for travelers with different origins and destinations. This paper proposes a method of approximating IPMC for general networks, in which a cell transmission model–based kinematic wave model is used to model traffic dynamics. By tracing the changes in the cumulative flow curves of the bottleneck links on which queues form during dynamic network loading, an approximation method is developed to obtain the IPMC for the cases of merge junctions, diverge junctions, and general junctions. This method was applied to compute the total path marginal cost in a network. The results showed that vehicles at the beginning of the congestion duration had significantly larger marginal travel costs than other vehicles. The method was then applied to solve a dynamic O-D estimation problem with partial link-flow counts and historical O-D trip tables. With the incorporation of IPMC into the estimation procedure, both the O-D demands and the observed path travel times were successfully reproduced.