IR-98-021 / May Estimation of Origin-Destination Matrices Using Traffic Counts – A Literature Survey

The estimation or updating of trip matrices using traffic counts is an important problem that has received much attention during recent years. It has been argued that one major advantage of the descent-based approach is its computational tractability. Descent-based approaches solve a so-called bilevel formulation of the trip matrix-estimation problem. The upper-level problem estimates the trip matrix while the lower-level problem is concerned with an assignment problem. In busy traffic regions, like Stockholm, it is realistic to take congestion into account. Route choices are assumed to follow Wardrop's (1952) user-equilibrium principle and, hence, methods based on equilibrium assignment of traffic are needed. In this chapter, we present applications of descent-based approaches to estimation problems of the Stockholm region using travel and network data from the year 1986. The Stockholm region is represented by a network consisting of 417 nodes and 964 road links with up to 2100 origin-destination pairs having a nonzero demand for traffic. The models are applied to the peak-hour period. The course of convergence is analysed and results compared. The results favour an approximate gradient approach, because of an effective and robust solution to the bilevel formulation provided. From the application of a method using second-order information, the uniqueness of the estimated trip matrix is not assured and, hence, possibly indicates multiple solutions.

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