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Pseudo-periodicity in a travel-time model used in dynamic traffic assignment



In the past several years, in network models for dynamic traffic assignment, link travel times have frequently been treated as a function of the number of vehicles on the link. In an earlier paper, the present authors considered the linear form of this link travel-time function and showed that if there is a step increase in the inflow pattern this causes an infinite sequence of steps or jumps in the outflow profile, gradually damping out over time. This paper extends the analysis of this phenomenon to nonlinear travel-time functions and to more general inflow patterns. We show that the phenomenon occurs with general travel-time functions, and occurs whether the flow changes in discontinuous steps or more smoothly, and whether flows increase or decrease. We illustrate the results with numerical examples. We find, and prove, some surprising results, in particular that, in the travel-time model, outflows can take a much longer time to adjust to small falls in inflows than to large falls in inflows.

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