This paper addresses the probabilistic properties of stochastic route choice set generation approaches. Such route sets need to be established for sake of estimation of route choice models as well as for prediction of route flows using such models. Due to the random process of stochastic choice set generation, the resulting route subset is a random variate both in terms of size, composition, and required number of random draws to achieve a predefined choice set. For sake of planning and execution of the generation process, more insight is needed in its probabilistic properties. Analytical analyses are performed to investigate a number of probabilistic properties regarding sample size, choice set size and composition for which mathematical expressions are developed. Some properties are applied to a grid network to show the practical use of the derived properties. Several important findings and rules are derived which can help govern the experimental set up of the route set generation process, one of which is the so-called n = 5k rule which means that as soon as the number of random draws n exceeds five times the size k of the generated choice set there is at least 90% confidence that the choice set is complete, that is all relevant alternatives have been selected. The paper shows that the general unequal selection probability case can very well be approximated by the equal selection probability case for which analytical expressions are derived.
Abstract