Some Consequences of Detailed Junction Modeling in Road Traffic Assignment

Until recently, analyses of the assignment problem have considered only restricted forms of the functions which relate the costs of travel to volumes of traffic. These analyses are not applicable to networks which include detailed models of either uncontrolled junctions or signal-control policies which react to changes in traffic volumes. Recent assignment procedures are capable of modeling both these kinds of junction interaction, and it is therefore of interest to determine under what conditions the behavior of such procedures is assured. In doing so, use is made of a recently established sufficient condition for good behavior in any network. In broad terms, this condition is that the cost of using a link depends mainly on the flow on that link. The condition is discussed, and a related but weaker condition is shown to be necessary to guarantee good behavior. Analysis of detailed models of priority junctions and roundabouts shows that they give rise to cost functions which just satisfy the necessary condition but fail to satisfy the sufficient one. At signal-controlled junctions, the policy which determines how the signal-settings are calculated influences whether or not these conditions are satisfied: various policies are analyzed, and all but one are shown to lead to a violation of the condition which is necessary for good behavior in any network.