How Much Urban Traffic is Searching for Parking? Simulating Curbside Parking as a Network of Finite Capacity Queues

With the increasing availability of transaction data collected by digital parking meters, paid curbside parking can be advantageously modeled as a network of interdependent queues. In this article we introduce methods for analyzing a special class of networks of finite capacity queues, where tasks arrive from an exogenous source, join the queue if there is an available server or are rejected and move to another queue in search of service according to the network topology. Such networks can be useful for modeling curbside parking since queues in the network perform the same function and drivers searching for an available server are under combinatorial constraints and jockeying is not instantaneous. Further, we provide a motivating example for such networks of finite capacity queues in the context of drivers searching for parking in the neighborhood of Belltown in Seattle, Washington, USA. Lastly, since the stationary distribution of such networks used to model parking are difficult to satisfactorily characterize, we also introduce a simulation tool for the purpose of testing the assumptions made to estimate interesting performance metrics. Our results suggest that a Markovian relaxation of the problem when solving for the mean rate metrics is comparable to deterministic service times reflective of a driver's tendency to park for the maximum allowable time.