A maximum entropy-least squares estimator for elastic origindestination trip matrix estimation

摘要

In transportation subnetwork-supernetwork analysis, it is well known that the origin-destination (O-D) flow table of a subnetworkis not only determined by trip generation and distribution, but also by traffic routing and diversion, due to the existence ofinternal-external, external-internal and external-external flows. This result indicates the variable nature of subnetwork O-Dflows. This paper discusses an elastic O-D flow table estimation problem for subnetwork analysis. The underlying assumption isthat each cell of the subnetwork O-D flow table contains an elastic demand function rather than a fixed demand rate and thedemand function can capture all traffic diversion effect under various network changes. We propose a combined maximumentropy-least squares (ME-LS) estimator, by which O-D flows are distributed over the subnetwork so as to maximize the tripdistribution entropy, while demand function parameters are estimated for achieving the least sum of squared estimation errors.While the estimator is powered by the classic convex combination algorithm, computational difficulties emerge within thealgorithm implementation until we incorporate partial optimality conditions and a column generation procedure into thealgorithmic framework. Numerical results from applying the combined estimator to a couple of subnetwork examples show thatan elastic O-D flow table, when used as input for subnetwork flow evaluations, reflects network flow changes significantly betterthan its fixed counterpart.