Distributed computing approaches for large-scale probit-based stochastic user equilibrium problems

摘要

Applications of probit-based stochastic user equilibrium (SUE) principle on large-scale networks have been largely limited because of the overwhelming computational burden in solving its stochastic network loading problem. A two-stage Monte Carlo simulation method is recognized to have satisfactory accuracy level when solving this stochastic network loading. This paper thus works on the acceleration of the Monte Carlo simulation method via using distributed computing system. Three distributed computing approaches are then adopted on the workload partition of the Monte Carlo simulation method. Wherein, the first approach allocates each processor in the distributed computing system to solve each trial of the simulation in parallel and in turns, and the second approach assigns all the processors to solve the shortest-path problems in one trial of the Monte Carlo simulation concurrently. The third approach is a combination of the first two, wherein both different trials of the Monte Carlo simulation as well as the shortest path problems in one trial are solved simultaneously. Performances of the three approaches are comprehensively tested by the Sioux-Falls network and then a randomly generated network example. It shows that computational time for the probit-based SUE problem can be largely reduced by any of these three approaches, and the first approach is found out to be superior to the other two. The first approach is then selected to calculate the probit-based SUE problem on a large-scale network example.