On the Multi-class Percentile User Equilibrium Traffic Assignment Problem

摘要: Travelers often reserve a buffer time for trips sensitive to arrival time, being frequently reminded of the uncertainties in transportation system. This paper intends model effects this risk-taking behavior heterogeneous travelers. are assumed choose routes minimize percentile travel i.e. budget that ensures desired probability on-time arrival; doing so, they drive system user equilibrium (UE), which is an extension classic Wardrop equilibrium. The uncertainty supply incorporated by modeling capacity each road segment as random variable. density functions these variables specified exogenously with flow-dependent parameters. By directly convoluting link distributions, distribution route obtained. function derived from convolutions does not have closed form and may be monotone respect flow general. Numerical schemes proposed evaluate approximate its Jacobian through recursive convolutions. For two special cases analytical UE solutions obtained verified numerical experiments. analyzes indicate travelers higher always use more reliable route, everything else equal. A route-based algorithm solve variational inequality formulation problem. An important feature diagonal elements scale shift, mimics Quasi-Newton method traffic assignment demonstrated satisfactory convergence performance able achieve very precise all reported tests.