Allocation of street parking facilities in a capacitated network with equilibrium constraints on drivers’ traveling and cruising for parking

• Published in: Transportation research. Part C, Emerging technologies Vol. 101; pp. 181 - 207
• Main Authors: Du, Yuchuan, Yu, Shanchuan, Meng, Qiang, Jiang, Shengchuan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2019
• Subjects: Cruising for parking; Cyclic flows; Quantal response equilibrium; Stochastic user equilibrium; Street parking; Quantal response equilibrium; Stochastic user equilibrium; Cruising for parking; Street parking; Cyclic flows
• ISSN: 0968-090X; 1879-2359
• DOI: 10.1016/j.trc.2019.02.015

•Street parking facility allocation is evaluated with its impact on traffic condition.•Equilibrium condition is developed for both parkers and travelers in the network.•Heterogeneous quantal response equilibrium is made for non-cooperative parking game. This study presents a method of mathematical programs with equilibrium constraints (MPEC) to determine the optimal sites of street parking facilities in a working area where drivers travel through or cruise for parking spaces in the morning commute. The optimal sites of street parking facilities incur shortest queuing delay in the capacitated network. We first propose a variational inequality to formulate the heterogeneous quantal response equilibrium (HQRE) for parkers in non-cooperative parking game and the logit-based stochastic user equilibrium (SUE) for travelers traversing the area. The HQRE is developed under the “infinite cyclic flows” assumption, allowing all possible routes, containing the cyclic routes of all times including the infinite. Therefore boundedly rational parkers who search the same curb for more than once via cyclic cruising strategies can be modeled in the parking game. Then based on the equilibrium conditions, the MPEC was developed to minimize the total queuing delay for all drivers in the area. The radial basis function (RBF) model algorithm, one of the surrogate model-based algorithms, was proposed to iteratively solve the MPEC problem. A numerical example from a real working area is presented to illustrate the proposed MPEC problem. The numerical results show that the traffic flow increase caused by cruising for parking can be presented by our model. In addition, the appropriate allocation should avoid parking spaces at the curbs of arterial where travelers drive for traversing the area and the streets intersecting the arterial.