Planning of parking enforcement patrol considering drivers' parking payment behavior

This paper focuses on improving the effectiveness of parking enforcement patrol by optimizing the schedule of visit at each parking lot and the routing plan of patrol vehicles. Meanwhile, individual parking driver makes his/her parking payment decision based on knowledge of the patrol visit frequencies. Game-theoretic models are proposed to capture the interactions among the parking enforcement agency and parking drivers. We first develop a discrete formulation of the problem in the form of a mixed-integer program and propose a Lagrangian relaxation based solution approach. For large-scale instances, we also develop a continuum approximation model that can be reduced to a simpler non-linear optimization problem. A series of numerical experiments are conducted to show that, for small problem instances, both modeling approaches can yield reasonable solutions, although the continuum approximation approach is able to produce a solution within a much shorter time. For large-scale instances, the discrete model incurs prohibitive computational burdens, while the continuum approximation approach still provides a near-optimum solution effectively. We also discuss impacts of various system parameters, as well as the performance of different policy options (e.g., whether to allow multiple parking tickets to be issued to a vehicle with a long time of parking violation).