Combined Dynamics of Route Choice and Gap Acceptance in Road Networks with Priority Intersections

A key determinant of the capacity of unsignalized intersection approaches operating under priority control is the gap acceptance behavior of drivers. The parameter commonly used to characterize this behavior is the critical gap, which is the minimum time interval in the priority traffic stream that minor road drivers consider acceptable to safely execute the desired maneuver. When the operation of priority intersections is considered in a network-wide perspective, the analysis of the interaction between gap acceptance behavior and route choice emerges as a compelling research question. This paper proposes a model of the day-to-day dynamics arising from this interaction when the critical gap of minor road drivers is treated as an endogenous variable. We formulate a discrete-time, deterministic nonlinear dynamical system in which the critical gap depends on the traffic flow on the major road. After providing a general formulation of the model, an explicit analysis of fixed-point stability is carried out for an elementary network. Numerical results obtained from the implementation on two example networks suggest that the evolutionary dynamics of the system are affected by the relationship between the critical gap and major road flow. We conclude that, upon proper calibration of the variable critical gap formulation on observed driver behavior, the proposed model has the potential to deliver improved estimates of intersection approach capacities, delays and queue lengths to be used for policy evaluation in a dynamic perspective.