The Network Cost of Congestion: Analysis and Computation of Marginal Social Cost Disaggregated by O-D Pair and Departure Time

The Network Cost of Congestion: Analysis and Computation of Marginal Social Cost Disaggregated by O-D Pair and Departure Time


F Leurent, Paris Tech-ENPC-LVMT, FR


Based on Leurent?s dynamic traffic assignment model (2003), a method is introduced to com-pute the marginal social cost of any trip with respect to its path and entry time. Application to the Seine-et-Marne road network is reported.


The extension of congestion over transportation networks, either car or public transport, has become a common feature of many cities and interurban corridors. Many schemes have been proposed, and often implemented, to manage it, from capacity investment to user information and orientation, passing by junction regulation, ramp-metering and pricing.
These schemes are based on the classical economists? recommendation to minimize the global social cost of traffic and congestion, including travel expense, time loss, safety, ecologic im-pacts. In order to achieve social efficiency, a trip should be charged by a fee equal to the mar-ginal social cost that the trip-maker imposes to the other stake-holders. At the level of a net-work arc, several economic papers have made clear how to compute the marginal social cost in a static or dynamic framework.
The purpose of the paper is to make an inquiry into the spatial structure of the traffic flows which contribute to congestion, in the dynamic framework of a network assignment model. A method is provided to compute the marginal cost induced by any trip on the basis of its route and timing, which enables one to design management schemes at the level of the origin-destination pair as well as time-of-day.
The method for analysis and computation of the marginal social cost of a trip according to its path and initial instant is as follows. On each network arc, the congestion state is modelled by the temporal profiles of the entry flow, exit flow, travel time, eventual delay and queue length, by user class: these enable us to compute the marginal social cost of any trip entering the arc at a selected instant (Leurent, 2003). Then, at the network level the marginal cost of entering a selected path at a selected, reference instant is the sum of the marginal costs along the arcs which make up the path, at those instants of arc entry which are implied by the reference in-stant due to traffic propagation.
The paper is structured in three sections.
Section I contains the analysis of marginal social cost in the framework of the dynamic traffic assignment of Leurent (2003): first the case of an isolated arc is addressed (Leurent 2005); then the network case is developed with full generality. Two alternative models are consid-ered for traffic flowing at the arc level, with either vertical queuing or horizontal queuing.
In Section II, the computation method is provided in the guise of a flowchart; then it is ap-plied to a classroom case. Some application guidance is also reported.
Section III provides an application to a real road network, which consists of the major routes in the French County ?Seine et Marne?: around one thousand kilometres of roads, including two motorways which connect the Paris area to the Eastern French regions.


Association for European Transport