Journal
MATHEMATICAL PROGRAMMING
Volume 101, Issue 1, Pages 205-230Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-004-0542-7
Keywords
transit networks; equilibrium assignment; strategy; hyperpath; capacities; priorities; variational inequalities
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In a transit network involving vehicles with rigid capacities, we advocate the use of strategies for describing consumer behavior. At each boarding node, a user sorts the transit lines in decreasing order of preference, and boards the first vehicle in this list whose residual capacity is nonzero. Since a user's position in the queue varies from day to day, the delay experienced is stochastic. This leads to an equilibrium problem where, at a solution. users are assigned to strategies that minimize their expected delay. This situation is formulated as a variational inequality, whose cost mapping is discontinuous and strongly asymmetric, due to the priority of cur-rent passengers over incoming users. We prove that the solution set is nonempty and provide numerical results obtained by an efficient solution algorithm.
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