Equilibrium characterization and computational solutions for departure time choice with two-dimensional heterogeneity

Vickrey's bottleneck, with a departure time choice equilibrium, is a classic model in transportation science.  We consider a variation of this model where travelers are heterogeneous in their aversion to early or late arrival at the destination.  Unlike past research, we consider a fairly general case of heterogeneity, requiring only that the support of the distribution of these parameters be bounded.  We introduce the concept of a "proper division" that converts questions of equilibrium existence, uniqueness, and computation into easier questions regarding existence, uniqueness, and computation of a proper division.  Using this technique, we show that there can be at most one equilibrium.  For the case of a discrete distribution over finitely many points, we present an efficient algorithm for computing equilibrium.


Dr. Stephen D. Boyles is Distinguished Teaching Professor and Clyde E. Lee Endowed Professor and Distinguished Teaching Professor in the Fariborz Maseeh Department of Civil, Architectural, and Environmental Engineering at The University of Texas at Austin, and an affiliate faculty member with the Operations Research and Industrial Engineering program.  His research and teaching are in transportation planning, optimization, game theory, and network algorithms.  He is lead author of the "Transportation Network Analysis" textbook and has received many awards in teaching, research, university service, and professional service, including being inducted into UT Austin's Academy of Distinguished Teachers, four best paper awards, and six national thesis awards for students he supervised.  He is licensed as a Professional Engineer in the state of Texas, and has provided occasional consulting services in transportation data science and analysis.