Modeling Curbside Parking as a Network of Finite Capacity Queues

Abstract

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.

Intelligent Management of On-street Parking Provision for the Autonomous Vehicles Era

“…Previous research concerning the on-street parking problem predominantly concentrates on three areas: the demand, supply and pricing for parking [15], [16]; safety and delay impacts of curb parking behaviours [17], [18]; the impact of on-street parking on traffic operations [19], [20]. A subset of studies from the third group has investigated how onstreet parking patterns can have an impact on such traffic operations [21]- [23].…”

Performance Evaluation of Stochastic Systems with Dedicated Delivery Bays and General On-Street Parking

“…In the existing literature, various queueing models have been studied for parking systems, among which the M=M=c=c queue is the most widely used model (Hauer and Templeton 1972;Caliskan et al 2007;Dalla Chiara and Cheah 2017;Dowling, Ratliff, and Zhang 2019). Wigan and Broughton (1980) use a discrete-time semi-Markov chain to investigate the occupancy of a parking area over time by allowing variations in the arrival of vehicles and their lengths of stay.…”

“…In addition, they show numerically that their proposed model-based predictive method performs better than pure machine learning parking occupancy prediction methods. In a recent study, Dowling, Ratliff, and Zhang (2019) examined curbside parking as a network of finite capacity queues, where performance metrics such as the rate of rejection of vehicles searching for parking and the parking occupancy were estimated using a simulation. In our paper, we consider both freight vehicles conducting delivery activities and passenger vehicles seeking parking space.…”

“…In parcel delivery (mostly due to online commerce), vehicles in Amsterdam have been reported to be parked for about 70% of total time spent on their route. Because it is very difficult to find parking space, vehicles are searching for parking space extensively (Cassady and Kobza 1998;Shoup 2006;Dowling, Ratliff, and Zhang 2019;Dalla Chiara and Goodchild 2020) and may be forced to park illegally causing difficulties to other traffic (Kladeftiras andAntoniou 2013, Gao andOzbay 2016). In a field experiment, Fransoo, Cedillo-Campos, and Gamez-Perez (2021) show that by providing more delivery bay space, efficiency improvements in deliveries of up to 40% could be reached.…”

“…Such curbside parking stretches that have both delivery bays and general-purpose street parking spaces with stochastic arrival and service times are complex systems to model. Earlier studies (Wigan and Broughton 1980;Caliskan et al 2007;Larson and Sasanuma 2007;Dalla Chiara and Cheah 2017;Xiao, Lou, and Frisby 2018;Dowling, Ratliff, and Zhang 2019) have investigated either freight delivery parking systems or on-street passenger vehicle (car) parking systems. However, as described above, in actual curbside parking stretches, delivery vehicles make use of both delivery bays and of general on-street parking spaces.…”