A PROBIT-BASED STOCHASTIC USER EQUILIBRIUM ASSIGNMENT MODEL

Stochastic methods of traffic assignment have received much less atten tion in the literature than those based on deterministic user equilibr ium (UE). The two best known methods for stochastic assignment are tho se of Burrell and Dial, both of which have certain weaknesses which ha ve limited their usefulness. Burrell's is a Monte Carlo method, whilst Dial's legit method takes no account of the correlation, or overlap, between alternative routes. This paper describes, firstly, a probit st ochastic method (SAM) which does not suffer from these weaknesses and which does not require path enumeration. While SAM has a different rou te-finding methodology to Burrell, it is shown that assigned flows are similar. The paper then goes on to show how, by incorporating capacit y restraint (in the form of link-based cost-flow functions) into this stochastic loading method, a new stochastic user equilibrium (SUE) mod el can be developed. The SUE problem can be expressed as a mathematica l programming problem, and its solution found by an iterative search p rocedure similar to that of the Frank-Wolfe algorithm commonly used to solve the UE problem. The method is made practicable because quantiti es calculated during the stochastic loading process make the SUE objec tive function easy to compute. As a consequence, at each iteration, th e optimal step length along the search direction can be estimated usin g a simple interpolation method. The algorithm is demonstrated by appl ying it successfully to a number of test problems, in which the algori thm shows good behaviour. It is shown that, as the values of parameter s describing the variability and degree of capacity restraint are vari ed, the SUE solution moves smoothly between the UE and pure stochastic solutions. (C) 1997 Elsevier Science Ltd.