Traffic Equilibrium in a Network Model of Parking and Route Choice, with Search Circuits and Cruising Flows

The paper provides a novel network model of parking and route choice. Supply is represented by parking type, management strategy including the fare, capacity and occupancy rate of parking lot, and network location, in relation to access routes. Demand is addressed in a disaggregate way according to the disposal of private parking facilities and the individual preferences for parking quality of service. Search circuits are explicitly considered on the basis of the success probability to get a slot at a given lot and transition probabilities between lots in case of failure. The basic model variables are the route flows, success probabilities and transition probabilities. These give rise to the cost of a travel route up to a target lot and to the expected cost of search and park from that lot. Each traveller is assumed to make a two stage choice of, first, network route on the basis of the expected overall route costs and, second, local diversion on the basis of a discrete choice model. Traffic equilibrium is defined in a static setting. It is characterized by a mixed problem of variational inequality and fixed point. Equilibrium is shown to exist under mild conditions and a Method of Successive Averages is put forward to solve for it. Lastly, a stylised instance is given to illustrate the effects of insufficient parking capacity on travel costs and network flows.