Mathematical models and computational algorithms for probit-based asymmetric stochastic user equilibrium problem with elastic demand

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Abstract
This article addresses model development and computational algorithm design for the probit-based asymmetric stochastic user equilibrium (SUE) problem with elastic demand. Two variational inequality (VI) models are first proposed for the SUE problem and then existence and uniqueness of their solutions are examined. These two VI models are, in reality, built by means of a probit-based stochastic network loading (SNL) map. Since there is no computational procedure available for calculating the SNL map, we thus propose a two-stage Monte Carlo simulation-based method to estimate the SNL map. To compromise computational time with accuracy in the estimation, a lower bound of sample size required by the Monte Carlo simulation is also investigated. Based on these two VI models and Monte Carlo simulation-based method, we design two hybrid prediction–correction (PC) — cost averaging (CA) algorithms for solving the SUE problem. Finally, two numerical examples are carried out to assess performance of the proposed algorithms.

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