Some remarks on Stochastic User Equilibrium

The behavioural foundation of Stochastic User Equilibrium is that each traveller attempts to minimize his or her perceived travel costs, where these costs are composed of a deterministic measured cost and a random term which can be interpreted as perceptual error. In principle such a definition, which is in terms of random errors, should imply an equilibrium probability distribution over feasible flow patterns on the transport network. Such a probability distribution could potentially allow between day variability in network flows to be represented. However, traditionally a deterministic, large sample approximation has been used as the ‘solution’ of Stochastic User Equilibrium. In this paper a representation of Stochastic User Equilibrium as a probability distribution is developed. This distribution is defined by the conditional route selection of each individual given the choices of all other travellers. An interpretation of the resulting assignment model as the limit (in the infinite future) of a continuous time assignment process is discussed. The limiting behaviour as the travel demand becomes large is also investigated, and convergence to the traditional deterministic form of Stochastic User Equilibrium is proved.