Total Travel Cost in Stochastic Assignment Models

Deterministic assignment models are sometimes used to approximate properties of more complex stochastic models. One property that is of particular interest from a system optimization viewpoint is total travel cost. This paper looks at the approximation of mean total travel cost. It is shown that deterministic models will underestimate this quantity in many common situations. Furthermore, discrepancies between total travel cost under the different modelling frameworks can lead to situations in which network modifications which are detrimental according to a stochastic model appear beneficial when using the natural deterministic approximation. We conclude that estimation of mean travel cost in stochastic assignment is often best done using simulation. Some suggestions are made regarding the implementation of traffic assignment simulation.