A splitting rate model of traffic re-routeing and traffic control

The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions repeated application of the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios. The paper sets the scene by giving a simple motivating model, involving both routeing changes and green-time changes following the equisaturation policy, in which unpredictable discontinuous behaviour, including a pitchfork bifurcation, occurs as a result of the interaction between re-routeing and responsive control.