Article ID: | iaor1996946 |
Country: | Switzerland |
Volume: | 60 |
Issue: | 1 |
Start Page Number: | 59 |
End Page Number: | 72 |
Publication Date: | Dec 1995 |
Journal: | Annals of Operations Research |
Authors: | Smith M.J., Wisten M.B. |
Suppose that a road network model is given, together with some given demand for travel by (say) car and that the demand for travel varies with time of day but not from day to day. Suppose that this demand is given in the form of specified total outflow rates from each origin headed towards each destination, for each origin-destination pair and for each time of day, and that some initial time-dependent route-inflow rates, meeting the given demand, are given. Finally, suppose that within-day time is represented by a continuous variable. This paper specifies a natural smooth day-to-day route-swapping procedure wherein drivers swap toward less expensive routes as day succeeds day, and shows that under reasonable conditions there is an equilibrium state of this dynamical system. If such a collection of route-inflows has arisen today, say, then there is no incentive for any route-inflow to change tomorrow, in the sense that at each moment of today each of today’s route-inflows is