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 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 also 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. © 2011 Elsevier Ltd.
Smith, M., & Mounce, R. (2011). A splitting rate model of traffic re-routeing and traffic control. Transportation Research Part B: Methodological, 45 `(9), 1389–1409. https://doi.org/10.1016/j.trb.2011.05.013