QUEUE SPILLOVERS IN TRANSPORTATION NETWORKS WITH A ROUTE CHOICE

This paper explores some of the traffic phenomena that arise when driv ers have to navigate a network in which queues back up past diverge in tersections. Ifa diverge provides two alternative routes to the same d estination and the shorter route has a bottleneck that generates a que ue, one would expect that queue to stabilize at an equilibrium level w here the travel time on both routes is roughly equal. If the capacity of the alternative route is unlimited then, this network can accommoda te any demand level. However, if the bottleneck is so close to the ups tream end of the link that the equilibrium queue cannot be contained i n the link, then, the trip time on the queued route cannot grow to mat ch that on the alternate route. This means that the alternative route can never be attractive, even if the queue spills back past the diverg e, and that drivers approaching the diverge will act as if the alterna tive route did not exist. As a result, a steady flow into the system g reater than the capacity of the bottleneck will cause a queue to grow all the way back to the origin (blocking it). The final result is an ' 'oversaturated static state'' where the queue regulates the input flow into the system. Curiously, if the bottleneck capacity of this networ k is reduced below a critical level (or is eliminated altogether) then . the alternative route becomes attractive again and the system cannot reach the saturation point. This phenomenon is explored in the paper, where it is also shown that:i) a network can become permanently overs aturated/undersaturated as a result of a temporary increase/decrease i n link capacity, ii) even under the most favorable assumptions, and in contrast to the equivalent assignment problem with point queues, a ne twork can be stable both in an oversaturated and an, undersaturated st ate, and iii) temporary endogenous disturbances can permanently revers e the saturation state of a network. These findings suggest that in ce rtain situations the time-dependent traffic assignment problem with ph ysical queues is chaotic in nature and that (as in weather forecasting ) it may be impossible to obtain input data with the required accuracy to make reliable predictions of cumulative output flows.