Parking search equilibrium on a network

• Parking search is integrated into traffic assignment with a network transformation.
• Parking search is stochastic, and drivers' policies form an equilibrium.
• The resulting flow conservation constraints are nonlinear.
• Mathematical properties of this equilibrium formulation are explored.
• A small demonstration shows how the model may be applied in practice.

This paper describes an equilibrium formulation for incorporating parking search into traffic network assignment models. The proposed model allows general network topologies and reflects uncertainty related to parking availability, including the possibility of cycling behavior as drivers search for parking. The equilibrium framework represents the mutual dependence between the probabilities of finding parking at different locations and the search processes employed by drivers to minimize total expected journey time (or cost). In this framework, network loading is represented by a system of nonlinear flow conservation networks, and feasibility and uniqueness issues are discussed. The equilibrium problem is formulated as a variational inequality and a convex combinations heuristic is proposed. Numerical results show that neglecting parking search can substantially underestimate network flows, and quantitatively demonstrate the relationship between parking duration effects and the cost of time spent walking relative to driving, and the expected driving and walking times.