An efficient path-storing equilibration algorithm is presented to solve a dual criteria assignment model with continuously distributed values of time. Applications include a sensitivity analysis and propagation of errors. A traffic assignment model is of particular interest to assess the traffic of a motorway project; it usually rests on the assumption that every trip-maker tries to minimize their generalized travel times, evaluated with respect to a uniform cost function. A dual criteria model enables an analyst to represent disaggregate trade-offs between two cost criteria, e.g. time and price in the cost vs time model. A fixed-times dual criteria model was first introduced to address the competition address the competition between the train and the plane in inter-regional transport (March, 1973). Then a mathematical formulation was designed to address both flow-dependent travel times and the elasticity of demand (Leurent, 1993a, 1993b). This paper includes two contributions to the practice of dual criteria assignment. First, a path-identifying algorithm is presented, wherein a generalized impedance is equalised between available paths: it is shown, based on a medium-size application (104 OD zones and 2,000 links) on a PC micro-computer, that this algorithm compares very favourably to the conventional, Frank-Wolfe procedure applied to the uniform, single value-of-time model of Wardrop and Beckmann. Second, a sensitivity analysis is worked out, in order to address issues like the uncertainty about the predicted revenue of a tolled urban motorway, due to the uncertainty about the distribution of the value-of-time across the trip-makers. (A)
Abstract