A STOCHASTIC MARKOVIAN APPROACH TO TRIP DISTRIBUTION

Abstract

Experience with trip-distribution models shows that the discrepancy between actual and estimated values of trip production, attraction, decay, and interchange cannot be completely eliminated. To improve upon this situation, this paper attributed a random structure to the trip-generation process by introducing a random error. Within this stochastic context, it was possible to develop a solution procedure to the trip-distribution problem based on a Markovian travel demand model, using only aggregate time-series trip-generation data. The proposed procedure is based on statistical estimation minimizing the errors sum of squares associated with the flow conservation constraint on trip attraction, subject to the trip-production flow constraint and a given trip-decay function. It is noteworthy to observe that the random error can be introduced into the trip-decay constraint or the trip-production constraint to generate the objective function to be minimized. The choice of the appropriate objective should be based on the predictive ability and the computational efficiency of the solution procedures associated with each of these two alternatives. The performance and efficiency of the proposed solution procedure in comparison with existing techniques have still to be demonstrated through empirical testing and computational experience. The model presented here, however, has a theoretical basis sound enough to suggest that an improvement in the efficiency of the resulting solution procedures could be expected in its application.