考虑用户成本和泊位利用率的停车预约分配模型

doi:10.13229/j.cnki.jdxbgxb.20230682

摘要/Abstract

摘要：

为提高停车资源利用率以缓解停车供需失衡问题，考虑停车分配过程中用户利益与系统效益间的博弈关系，建立了预约模式下停车泊位利用率最大和用户成本最小的联合优化目标函数；构建了融合用户偏好特性的最优停车分配整数规划模型（OPA），并设计了增广拉格朗日-交替乘子算法进行预约泊位分配方案求解。为检验模型的有效性，在不同停车供需情况下将本文模型与多种经典停车分配模型对比，结果表明：本文OPA模型在泊位利用率、用户平均成本和请求接收率3个评价指标上的表现均明显优于经典分配模型，本文研究成果可为停车预约平台的决策管理提供理论参考。

关键词: 交通运输系统工程, 停车分配, 整数规划模型, 增广拉格朗日-交替乘子算法

Abstract:

In order to alleviate the problem of imbalance between parking supply and demand by improving the utilization rate of parking resources， and considering the game relationship between user benefits and system benefits in parking allocation， the optimization objective function of maximum parking space utilization and minimum user cost in parking reservation mode is established from the two aspects which are system optimization and user optimization respectively. Then， the optimal parking allocation integer programming model（OPA） considering users' preferences is established. An Augmented Lagrangian-Alternating Direction Method of Multipliers Algorithm is designed to solve the optimal solution of the model. Finally， in order to test the validity of the model， the proposed model and the classical distribution model are compared and analyzed under different supply and demand conditions. The results show that the performance of the proposed model in three performance metrics which are parking utilization， average user cost and request acceptance rate is significantly better than that of the classical allocation model. The research results of this paper can provide theoretical reference for the management of parking reservation platform.

Key words: engineering of communication and transportation, parking allocation, integer programming model, augmented Lagrangian-alternating direction method of multipliers algorithm

中图分类号:

U491.5

宋现敏,湛天舒,李海涛,刘博,张云翔. 考虑用户成本和泊位利用率的停车预约分配模型[J]. 吉林大学学报(工学版), 2025, 55(4): 1287-1297.

Xian-min SONG,Tian-shu ZHAN,Hai-tao LI,Bo LIU,Yun-xiang ZHANG. Reservation and allocation model considering user cost and utilization of parking space[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(4): 1287-1297.

图/表 13

图1

表1

变量、参数定义"

符号	定义
$T$ /h	系统中一天的泊位可用总时长
$t$ /min	系统设定的单位时段长度
$K$	一天的单位时段个数
$k$	单位时段编号
$J$ /个	停车场总数
$j$	停车场编号
$N$	平台租用的泊位总数
$n$	泊位编号
$a n j$	停车泊位分布状态，若停车泊位 $n$ 属于停车场 $j$ ， $a n j = 1$ ；否则， $a n j = 0$
$s n k$	停车供给状态，若停车泊位 $n$ 在时间间隔 $k$ 可用， $s n k = 1$ ；否则， $s n k = 0$
$M *$ /个	停车请求总数
$m *$	停车请求编号
$t m * s t a r t, t m * e n d$	请求 $m *$ 的停车时段
$l m * m a x$ /m	请求 $m *$ 的最大可接受步行距离
$f m * m a x$ /（元·h^-1）	请求 $m *$ 的最高可接受停车费率
$d u r m *$ /	请求 $m $ 的停车时长， $d u r m = t m * e n d - t m * s t a r t + 1$
$x m , y m $	请求 $m *$ 的目的地中心坐标
$x j, y j$	停车场 $j$ 的中心坐标
$f j$ /（元·h^-1）	停车场 $j$ 的停车费率
$p j$ /（元·d^-1）	平台向停车场 $j$ 租用泊位时的租金
$l m * j$ /m	请求 $m *$ 的步行距离
$M$ /个	分配池中的请求总数
$m$	分配池中的请求编号
$d m k$	用户需求状态，若用户 $m$ 在时间间隔 $k$ 有停车需求，则 $d m k = 1$ ；否则， $d m k = 0$
$x m n$	停车分配结果，若用户 $m$ 被分配到泊位 $n$ ，则 $x m n = 1$ ；否则， $x m n = 0$
$X M × N$	停车分配矩阵， $X M × N = x m n$
$c m j$	停车场分配状态， $c m j = ∑ n = 1 N x m n · a n j$
$z n k$	泊位占用状态， $z n k = ∑ m = 1 M x n m · d m k$

表1

图2

图3

图4

表2

不同分配方法下的计算结果"

分配方法	评价指标
分配方法	$U$	$π ˉ$	$A$
OPA	0.85	7.68	0.82
FCFS	0.76	10.15	0.69
FBFS	0.73	9.01	0.72
GPA	0.73	8.25	0.75

表2

图5

图6

图7

图8

图9

图10

图11

参考文献 21

[1]	Shoup D. Cruising for parking[J]. Transport Policy, 2006, 13(6): 479-486.
[2]	宁瑞昌. 基于预约模式的停车选择模型研究[D]. 西安: 长安大学交通学院, 2017.
	Ning Rui-chang. Research on parking selection model based on reservation mode[D]. Xi´an: School of Transportation, Chang´an University, 2017.
[3]	He H, Zhang Z X, Yan P Y. A real-time reservation service for smart parking system[C]∥The 15th International Conference on Service Systems and Service Management (ICSSSM), Hangzhou, China, 2018: 1-6.
[4]	Said A M, Kamal A, Afifi H. An intelligent parking sharing system for green and smart cities based IoT[J]. Computer Communications, 2021, 172: 10-18.
[5]	盖松雪, 曾小清, 岳晓园, 等. 基于用户-系统双层优化算法的车位引导模型[J]. 吉林大学学报:工学版, 2022, 52(6): 1344-1352.
	Gai Song-xue, Zeng Xiao-qing, Yue Xiao-yuan, et al. Parking guidance model based on user and system bi⁃level optimization algorithm[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(6): 1344-1352.
[6]	Liu W, Graham D J, Yang H, et al. Modeling and managing the joint equilibrium of destination and parking choices under hybrid supply of curbside and shared parking[J]. Transportation Research Part C—Emerging Technologies, 2021, 130: No. 103301.
[7]	Zhang F N, Liu W, Wang X L, et al. Parking sharing problem with spatially distributed parking supplies[J]. Transportation Research Part C—Emerging Technologies, 2020, 117:No.102676.
[8]	Shao C Y, Yang H, Zhang Y, et al. A simple reservation and allocation model of shared parking lots[J]. Transportation Research Part C—Emerging Technologies, 2016, 71: 303-312.
[9]	Xie M H, Zhang X Y, Wu Z H, et al. A shared parking optimization framework based on dynamic resource allocation and path planning[J]. Physica D: Nonlinear Phenomena, 2023, 616: No.128649.
[10]	孙会君, 傅丹华, 吕莹, 等. 基于共享停车的泊位租用与分配模型[J]. 交通运输系统工程与信息, 2020, 20(3): 130-136.
	Sun Hui-jun, Fu Dan-hua, Ying Lyu, et al. Parking spaces renting and allocation model for shared parking[J]. Journal of Transportation Systems Engineering and Information Technology, 2020, 20(3): 130-136.
[11]	Zhao P F, Guan H Z, Wei H, et al. Mathematical modeling and heuristic approaches to optimize shared parking resources: a case study of Beijing, China[J]. Transportation Research Interdisciplinary Perspectives, 2021, 9: 2590-1982.
[12]	Wang S F, Li Z H, Xie N. A reservation and allocation model for shared-parking addressing the uncertainty in drivers' arrival/departure time[J]. Transportation Research Part C—Emerging Technologies, 2022, 135: No. 103484.
[13]	Kim O T T, Tran N H, Pham C, et al. Parking assignment: minimizing parking expenses and balancing parking demand among multiple parking lots[J]. IEEE Transactions on Automation Science and Engineering, 2020, 17(3): 1320-1331.
[14]	戴静. 居住区共享停车泊位分配模型研究[D]. 哈尔滨: 东北林业大学交通学院, 2018.
	Dai Jing. Shared parking spaces induction model in residential areas[D]. Harbin: School of Transportation, Northeast Forestry University, 2018.
[15]	Wang Y, Chen Q. Dynamic parking allocation model in a multidestination multiple parking lot system[J]. IEEE Intelligent Transportation Systems Magazine, 2022, 14(5): 195-208.
[16]	杨博. 基于时间窗约束的居住区共享停车泊位预订分配模型研究[D]. 北京:北京交通大学交通运输学院, 2018.
	Yang Bo. The study on shared parking slots allocation model for residential areas based on time window constraint[D]. Beijing: School of Transportation, Beijing Jiaotong University, 2018.
[17]	Choi H G, Seiler P J, Dhople S V. Propagating uncertainty in power flow with the alternating direction method of multipliers[J]. IEEE Transactions on Power Systems, 2018, 33(4): 4124-4133.
[18]	Jiang B W, Fan Z P. Optimal allocation of shared parking slots considering parking unpunctuality under a platform-based management approach[J]. Transportation Research Part E: Logistics and Transportation Review, 2020, 142:No. 102062.
[19]	Xie M H, Lin S Y, Wu Z H, et al. Optimal allocation and adjustment mechanism of shared parking slots considering combined parking resources[J]. Transportation Letters, 2023,15(7): 730-741.
[20]	Richardson A J. An improved parking duration study method[C]∥Proceedings of the 7th Australian Road Research Board Conference, Adelaide, Australia, 1974: 397-413.
[21]	Xue Z J, Cheng J H, Ji K F. An allocation model of shared parking with continuous time windows[C]∥Conference on Industrial Electronics and Applications, Chengdu, China, 2021:253-258.

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