Mj. Maher et Pc. Hughes, A PROBIT-BASED STOCHASTIC USER EQUILIBRIUM ASSIGNMENT MODEL, Transportation research. Part B: methodological, 31(4), 1997, pp. 341-355
Citations number
32
Categorie Soggetti
Transportation,"Operatione Research & Management Science","Engineering, Civil
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.