STATISTICAL PROPERTIES OF MATHEMATICAL PROGRAMMING MODELS OF STOCHASTIC NETWORK EQUILIBRIUM

ABSTRACT. Boyce et al. (1981, 1983) have proposed and implementd the use of observed entropy levels to estimate the travel‐cost coefficient in mathematical programming models of network equilibrium which involve logit route‐choice probabilities. This so‐called “dispersion‐constrained” model is shown to give severely biased and statistically inefficient underestimates. A natural counterpart, the entropy‐maximizing model, is proposed here and overestimates the travel‐cost coefficient with much lower bias and much higher statistical efficiency. Even though the two models are mathematically homeomorphic in some respects, they have vastly different statistical properties. It follows that the use of observed entropy levels is undesirable and should be avoided, since maximizing entropy provides an unambiguously superior alternative.