MAXIMUM ENTROPY PRINCIPLE FOR TRANSPORTATION

In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utility concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.