A user equilibrium, traffic assignment model of network route and parking lot choice, with search circuits and cruising flows

•Static user equilibrium under capacitated parking lots.•A user chooses a target parking lot and a path to it.•If parking fails at a lot then the user chooses another lot.•Search loops may arise from successive diversions.•Explicit formula for the expected cost from target lot to destination.

The paper provides a novel network model of parking and route choice. Parking 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 along the roadway network. Trip demand is segmented according to origin–destination pair, the disposal of private parking facilities and the individual preferences for parking quality of service. Each traveller is assumed to make a two stage choice of, first, network route on the basis of the expected cost of route and parking and, second, local diversion on the basis of a discrete choice model. Search circuits are explicitly considered on the basis of the success probability to get a slot at a given lot and of the transition probabilities between lots in case of failure.The basic endogenous model variables are the route flows, the lot success probabilities and the transition probabilities between lots. 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 to the destination. 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 planning instance is given to illustrate the effects of insufficient parking capacity on travel costs and network flows.