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Article(id=1149738769089216712, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738762382524507, articleNumber=1003-3033(2024)07-0178-08, orderNo=null, doi=10.16265/j.cnki.issn1003-3033.2024.07.0153, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1705248000000, receivedDateStr=2024-01-15, revisedDate=1713196800000, revisedDateStr=2024-04-16, acceptedDate=null, acceptedDateStr=null, onlineDate=1752048683664, onlineDateStr=2025-07-09, pubDate=1722096000000, pubDateStr=2024-07-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752048683664, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752048683664, creator=13701087609, updateTime=1752048683664, updator=13701087609, issue=Issue{id=1149738762382524507, tenantId=1146029695717560320, journalId=1146031787341344770, year='2024', volume='34', issue='7', pageStart='1', pageEnd='252', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752048682065, creator=13701087609, updateTime=1757316437713, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1171833331021824745, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738762382524507, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1171833331021824746, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149738762382524507, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=178, endPage=185, ext={EN=ArticleExt(id=1149738769311514834, articleId=1149738769089216712, tenantId=1146029695717560320, journalId=1146031787341344770, language=EN, title=Allocation of traffic police resources based on queuing theory, columnId=1149733270084042840, journalTitle=China Safety Science Journal, columnName=Public safety, runingTitle=null, highlight=null, articleAbstract=

To alleviate the contradiction between limited traffic police resources and the untimely handling of road traffic accidents，a traffic police resource optimization allocation approach was proposed based on a queuing theory model under a grid management mode of roads. Firstly，license plate recognition data obtained from the city's road network bayonet system was used to extract historical travel trajectories of vehicles and develop a similarity model between road segments. Secondly，the spectral clustering algorithm was adopted to cluster the road segments and form a set with the highest association between the segments，serving as the result of the road network division. Then，for the real-time traffic accidents within the grid，a queuing theory model was further proposed to calculate the minimum number of police officers required for each grid，along with an optimized allocation scheme for police resources. Finally，the proposed method was validated in Yinzhou District of Ningbo City. The results showed that the proposed optimization method for police allocation reduced the number of police officers by 18.18% and patrol mileage by 10.87% compared to the traditional method of dispatching police officers as soon as an accident occurs. Furthermore，the proposed method increased the accident handling response speed by 10.68%，demonstrating excellent optimization performance.

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为缓解有限的交通警力资源与道路交通事故处理不及时之间的矛盾，提出道路网格化管理模式下基于排队论模型的交通警力优化配置方法。首先，利用城市路网卡口系统获取的车牌识别数据，提取车辆的历史出行轨迹，建立路段之间的相似度模型；其次，采用谱聚类算法对路段进行聚类划分，形成路段之间关联度最高的集合，作为城市道路网格划分的结果；然后，针对网格范围内实时发生的交通事故，进一步提出利用排队论模型来计算每个网格所需的最少警员数量，以及相应的警力资源配置优化方案；最后，以宁波市鄞州区为例验证所提方法。结果表明：与传统的“事故即发生即派发警员”的方法相比，提出的警力资源配置优化方法能够减少18.18%的警员配置数量和10.87%的出警巡航路程，使事故处置的响应速度提高10.68%，表现出良好的优化性能。

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胡正华 (1986—)，男，浙江绍兴人，博士，副教授，主要从事交通地理信息科学、 人工智能、数据挖掘技术等方面的研究。E-mail：。

周继彪 副教授；

马昌喜 教授

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胡正华 (1986—)，男，浙江绍兴人，博士，副教授，主要从事交通地理信息科学、 人工智能、数据挖掘技术等方面的研究。E-mail：。

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胡正华 (1986—)，男，浙江绍兴人，博士，副教授，主要从事交通地理信息科学、 人工智能、数据挖掘技术等方面的研究。E-mail：。

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Index names and their interpretations

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类目 变量名 含义
索引 S 网格(即交警中队的管辖区域)
I 网格的总数
i 网格S的索引
J 时间窗内网格Si总共发生的
交通事故数量
j 在网格Si内发生事故的索引
k 在网格Si内派遣警员的索引
参数 Z ( S i ) 网格Si需要派遣的警员数
A j S i 网格Si内发生的第j起事故
L 警员当前所在的位置
v -/(km·h-1) 警员的平均行驶速度
P(A，B)/km 地点A与B之间的最短路径
C k S i 第k个警员在网格Si内累
计处理的交通事故数
N+ 非零自然数集合
Q 需要处理的交通事故队列
T/h 处理一起事故的平均时间
T(M)/h 处理“物损事故”所需的时间
T(C)/h 处理“伤亡事故”所需的时间
T( A c S i，k)/h 网格Si内第k个警员处理完第c
起事故还需要的时间
), ArticleFig(id=1168186507505443102, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738769089216712, language=CN, label=表1, caption=

索引名称及含义

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类目 变量名 含义
索引 S 网格(即交警中队的管辖区域)
I 网格的总数
i 网格S的索引
J 时间窗内网格Si总共发生的
交通事故数量
j 在网格Si内发生事故的索引
k 在网格Si内派遣警员的索引
参数 Z ( S i ) 网格Si需要派遣的警员数
A j S i 网格Si内发生的第j起事故
L 警员当前所在的位置
v -/(km·h-1) 警员的平均行驶速度
P(A，B)/km 地点A与B之间的最短路径
C k S i 第k个警员在网格Si内累
计处理的交通事故数
N+ 非零自然数集合
Q 需要处理的交通事故队列
T/h 处理一起事故的平均时间
T(M)/h 处理“物损事故”所需的时间
T(C)/h 处理“伤亡事故”所需的时间
T( A c S i，k)/h 网格Si内第k个警员处理完第c
起事故还需要的时间
), ArticleFig(id=1168186507568357663, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738769089216712, language=EN, label=Table 2, caption=

Constraints content

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序号 约束条件的内容
1 根据宁波市公安局交通警察局的规定
(简称规定)，交警在接到当事人报警后，
须在10 min之内到达现场
2 每一位交警不跨格网执行任务
3 根据规定，每位交警一天最多只能处理8起事故
4 根据规定，物损事故按照10 min处理完毕，
伤亡事故按照20 min处理完毕
5 如果发生伤亡事故，直接插入Q的头部优
先处理；否则按照发生的时间顺序进入Q
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约束条件内容

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序号 约束条件的内容
1 根据宁波市公安局交通警察局的规定
(简称规定)，交警在接到当事人报警后，
须在10 min之内到达现场
2 每一位交警不跨格网执行任务
3 根据规定，每位交警一天最多只能处理8起事故
4 根据规定，物损事故按照10 min处理完毕，
伤亡事故按照20 min处理完毕
5 如果发生伤亡事故，直接插入Q的头部优
先处理；否则按照发生的时间顺序进入Q
), ArticleFig(id=1168186507698381089, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738769089216712, language=EN, label=Table 3, caption=

Comparision of traffic police dispatch plans between queuing theory and traditional model

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序
号		 发生时间 出警的警
员编号		 所属
网格		 出行距离/m 到达时间 结束时间 等待时间
(a) (b) (a) (b) (a) (b) (a) (b) (a) (b)
1 7:10:00 1 1 网格1 899 899 7:11:04 7:11:04 7:31:04 7:31:04 0:01:04 0:01:04
2 7:20:00 2 2 网格1 7 075 7 075 7:28:29 7:28:29 7:38:29 7:38:29 0:08:29 0:08:29
3 7:24:00 3 3 网格1 2 633 2 633 7:27:09 7:27:09 7:37:09 7:37:09 0:03:09 0:03:09
4 7:38:00 6 7 网格4 6 336 6 336 7:45:36 7:45:36 7:55:36 7:55:36 0:07:36 0:07:36
5 7:49:00 8 9 网格3 2 441 2 441 7:51:55 7:51:55 8:01:55 8:01:55 0:02:55 0:02:55
6 8:00:00 4 5 网格2 6 487 6 487 8:07:47 8:07:47 8:17:47 8:17:47 0:07:47 0:07:47
7 8:01:00 9 10 网格3 2 895 2 895 8:04:28 8:04:28 8:14:28 8:14:28 0:03:28 0:03:28
8 8:04:00 6 8 网格4 3 226 5 852 8:07:52 8:11:01 8:17:52 8:21:01 0:03:52 0:07:01
9 8:04:00 8 11 网格3 2 602 3 312 8:07:07 8:07:58 8:17:07 8:17:58 0:03:07 0:03:58
10 8:10:00 5 6 网格5 4 651 4 651 8:15:35 8:15:35 8:25:35 8:25:35 0:05:35 0:05:35
11 8:15:00 9 9 网格3 4 860 3 630 8:20:50 8:19:21 8:30:50 8:29:21 0:05:50 0:04:21
12 8:20:00 8 10 网格3 2 338 3 410 8:22:48 8:24:05 8:32:48 8:34:05 0:02:48 0:04:05
13 8:22:00 1 1 网格1 5 955 5 635 8:29:09 8:28:45 8:39:09 8:38:45 0:07:09 0:06:45
14 8:24:00 6 7 网格4 1 106 5 479 8:25:19 8:30:34 8:45:19 8:50:34 0:01:19 0:06:34
15 8:30:00 2 2 网格1 4 945 2 633 8:35:56 8:33:09 8:45:56 8:43:09 0:05:56 0:03:09
16 8:32:00 9 11 网格3 7 494 4 116 8:40:59 8:36:56 8:50:59 8:46:56 0:08:59 0:04:56
17 8:35:00 7 8 网格4 4 504 4 504 8:40:24 8:40:24 8:50:24 8:50:24 0:05:24 0:05:24
18 8:36:00 3 3 网格1 3 920 4 781 8:40:42 8:41:44 8:50:42 8:51:44 0:04:42 0:05:44
19 8:40:00 1 4 网格1 4 213 1 633 8:45:03 8:41:57 8:55:03 8:51:57 0:05:03 0:01:57
20 8:40:00 4 5 网格2 15 6 503 8:40:01 8:47:48 8:50:01 8:57:48 0:00:01 0:07:48
21 8:46:00 5 6 网格5 1 850 5 353 8:48:13 8:52:25 8:58:13 9:02:25 0:02:13 0:06:25
— 出行总
路程		 80 445 90 258 — 平均等
待时间		 0:04:36 0:05:09
提升占
比/%		 — 10.87 提升占
比/%		 — 10.68
), ArticleFig(id=1168186507815821602, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149738769089216712, language=CN, label=表3, caption=

排队论模型的警员出警方案与传统模式的出警方案比较

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序
号		 发生时间 出警的警
员编号		 所属
网格		 出行距离/m 到达时间 结束时间 等待时间
(a) (b) (a) (b) (a) (b) (a) (b) (a) (b)
1 7:10:00 1 1 网格1 899 899 7:11:04 7:11:04 7:31:04 7:31:04 0:01:04 0:01:04
2 7:20:00 2 2 网格1 7 075 7 075 7:28:29 7:28:29 7:38:29 7:38:29 0:08:29 0:08:29
3 7:24:00 3 3 网格1 2 633 2 633 7:27:09 7:27:09 7:37:09 7:37:09 0:03:09 0:03:09
4 7:38:00 6 7 网格4 6 336 6 336 7:45:36 7:45:36 7:55:36 7:55:36 0:07:36 0:07:36
5 7:49:00 8 9 网格3 2 441 2 441 7:51:55 7:51:55 8:01:55 8:01:55 0:02:55 0:02:55
6 8:00:00 4 5 网格2 6 487 6 487 8:07:47 8:07:47 8:17:47 8:17:47 0:07:47 0:07:47
7 8:01:00 9 10 网格3 2 895 2 895 8:04:28 8:04:28 8:14:28 8:14:28 0:03:28 0:03:28
8 8:04:00 6 8 网格4 3 226 5 852 8:07:52 8:11:01 8:17:52 8:21:01 0:03:52 0:07:01
9 8:04:00 8 11 网格3 2 602 3 312 8:07:07 8:07:58 8:17:07 8:17:58 0:03:07 0:03:58
10 8:10:00 5 6 网格5 4 651 4 651 8:15:35 8:15:35 8:25:35 8:25:35 0:05:35 0:05:35
11 8:15:00 9 9 网格3 4 860 3 630 8:20:50 8:19:21 8:30:50 8:29:21 0:05:50 0:04:21
12 8:20:00 8 10 网格3 2 338 3 410 8:22:48 8:24:05 8:32:48 8:34:05 0:02:48 0:04:05
13 8:22:00 1 1 网格1 5 955 5 635 8:29:09 8:28:45 8:39:09 8:38:45 0:07:09 0:06:45
14 8:24:00 6 7 网格4 1 106 5 479 8:25:19 8:30:34 8:45:19 8:50:34 0:01:19 0:06:34
15 8:30:00 2 2 网格1 4 945 2 633 8:35:56 8:33:09 8:45:56 8:43:09 0:05:56 0:03:09
16 8:32:00 9 11 网格3 7 494 4 116 8:40:59 8:36:56 8:50:59 8:46:56 0:08:59 0:04:56
17 8:35:00 7 8 网格4 4 504 4 504 8:40:24 8:40:24 8:50:24 8:50:24 0:05:24 0:05:24
18 8:36:00 3 3 网格1 3 920 4 781 8:40:42 8:41:44 8:50:42 8:51:44 0:04:42 0:05:44
19 8:40:00 1 4 网格1 4 213 1 633 8:45:03 8:41:57 8:55:03 8:51:57 0:05:03 0:01:57
20 8:40:00 4 5 网格2 15 6 503 8:40:01 8:47:48 8:50:01 8:57:48 0:00:01 0:07:48
21 8:46:00 5 6 网格5 1 850 5 353 8:48:13 8:52:25 8:58:13 9:02:25 0:02:13 0:06:25
— 出行总
路程		 80 445 90 258 — 平均等
待时间		 0:04:36 0:05:09
提升占
比/%		 — 10.87 提升占
比/%		 — 10.68
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基于排队论的道路交通警力资源配置研究
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胡正华 1 , 周继彪 2, 3 , 郭旭 1 , 马昌喜 4
中国安全科学学报 | 公共安全 2024,34(7): 178-185
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中国安全科学学报 | 公共安全 2024, 34(7): 178-185
基于排队论的道路交通警力资源配置研究
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胡正华1 , 周继彪2, 3, 郭旭1, 马昌喜4
作者信息
  • 1 宁波工程学院 网络空间安全学院，浙江 宁波 315211
  • 2 宁波市高等级公路建设管理中心，浙江 宁波 315199
  • 3 同济大学 交通运输工程学院，上海 201804
  • 4 兰州交通大学 交通运输学院，甘肃 兰州 730070

    • 胡正华 (1986—)，男，浙江绍兴人，博士，副教授，主要从事交通地理信息科学、 人工智能、数据挖掘技术等方面的研究。E-mail：。

    周继彪 副教授；

    马昌喜 教授

Allocation of traffic police resources based on queuing theory
Zhenghua HU1 , Jibiao ZHOU2, 3, Xu GUO1, Changxi MA4
Affiliations
  • 1 School of Cyber Science and Engineering，Ningbo University of Technology，Ningbo Zhejiang 315211，China
  • 2 Ningbo Highway Construction & Management Center，Ningbo Zhejiang 315199，China
  • 3 School of Transportation Engineering，Tongji University，Shanghai 201804，China
  • 4 School of Traffic and Transportation，Lanzhou Jiaotong University，Lanzhou Gansu 730070，China
出版时间: 2024-07-28 doi: 10.16265/j.cnki.issn1003-3033.2024.07.0153
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摘要
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为缓解有限的交通警力资源与道路交通事故处理不及时之间的矛盾，提出道路网格化管理模式下基于排队论模型的交通警力优化配置方法。首先，利用城市路网卡口系统获取的车牌识别数据，提取车辆的历史出行轨迹，建立路段之间的相似度模型；其次，采用谱聚类算法对路段进行聚类划分，形成路段之间关联度最高的集合，作为城市道路网格划分的结果；然后，针对网格范围内实时发生的交通事故，进一步提出利用排队论模型来计算每个网格所需的最少警员数量，以及相应的警力资源配置优化方案；最后，以宁波市鄞州区为例验证所提方法。结果表明：与传统的“事故即发生即派发警员”的方法相比，提出的警力资源配置优化方法能够减少18.18%的警员配置数量和10.87%的出警巡航路程，使事故处置的响应速度提高10.68%，表现出良好的优化性能。

排队论  /  交通警力  /  资源配置  /  交通事故  /  网格化管理

To alleviate the contradiction between limited traffic police resources and the untimely handling of road traffic accidents，a traffic police resource optimization allocation approach was proposed based on a queuing theory model under a grid management mode of roads. Firstly，license plate recognition data obtained from the city's road network bayonet system was used to extract historical travel trajectories of vehicles and develop a similarity model between road segments. Secondly，the spectral clustering algorithm was adopted to cluster the road segments and form a set with the highest association between the segments，serving as the result of the road network division. Then，for the real-time traffic accidents within the grid，a queuing theory model was further proposed to calculate the minimum number of police officers required for each grid，along with an optimized allocation scheme for police resources. Finally，the proposed method was validated in Yinzhou District of Ningbo City. The results showed that the proposed optimization method for police allocation reduced the number of police officers by 18.18% and patrol mileage by 10.87% compared to the traditional method of dispatching police officers as soon as an accident occurs. Furthermore，the proposed method increased the accident handling response speed by 10.68%，demonstrating excellent optimization performance.

queuing theory  /  traffic police  /  resource allocation  /  traffic accidents  /  grid-based management
胡正华, 周继彪, 郭旭, 马昌喜. 基于排队论的道路交通警力资源配置研究. 中国安全科学学报, 2024 , 34 (7) : 178 -185 . DOI: 10.16265/j.cnki.issn1003-3033.2024.07.0153
Zhenghua HU, Jibiao ZHOU, Xu GUO, Changxi MA. Allocation of traffic police resources based on queuing theory[J]. China Safety Science Journal, 2024 , 34 (7) : 178 -185 . DOI: 10.16265/j.cnki.issn1003-3033.2024.07.0153
正文
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0 引言
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随着国民经济的快速发展，城市的机动车保有量急剧增长，人们的生活也变得越来越便捷。但是迅速增长的机动车数量与有限的道路基础设施之间的矛盾也日趋明显，城市路网频繁出现交通拥堵[1]、交通秩序混乱[2]和交通事故频发[3]等一系列道路安全问题。据世界卫生组织统计，由于交通事故导致全球每年有130万人死亡和5 000万人受伤，经济损失总量超过5 000亿美元，交通事故已经成为人员意外伤亡的主导原因[4]。路网频繁发生的交通事故也给有限的警力资源调配带来巨大的压力，尤其是针对各类突发的重大交通事故，要求交警能够在最短的时间内到达事故现场，及时处理相应的事件，以避免因交通事故引发二次伤害[5]。
我国的交管部门一直存在着警力资源不足与人员配置不合理的现象，警力资源分散、出警不及时和警力资源不能共享等问题[6-7]严重制约着警务效能的提升，跨区域、跨部门的应急指挥调度依然存在着诸多不足。针对日益严重的交通安全问题与警力资源不足之间的矛盾，STEDEN等[8]提出招录警察志愿者并通过技能培训和提高薪酬的方式来提高他们的工作效率，以此缓解交通执法的压力；NEWSTEAD等[9]使用资源管理技术来提供警员长期、广泛的路网覆盖方案，以随机安排警察执法的方式最大化道路安全效益；李志恒等[10]在考虑交通信号灯的影响下，建立了交通警力的巡逻模型，使得交警巡逻的路线既能覆盖所有路段，又能使巡逻时间最短；ADLER等[11]利用线性规划的方法研究交警巡逻车辆的分配及路径规划问题，开发了位置分配模型并将其应用于实际的案例研究中；胡子峰[12]综合考虑了多种约束条件，以完成全部出警任务的总距离为代价建立巡逻路径的规划模型，并通过对智能算法的求解实现巡逻路径的规划；DUNNETT等[13]致力于通过运用覆盖优化模型来优化警力资源的分配，以提高交通事故的应对速度、缓解拥堵、提高交通安全等方面的效能。但面对实际应用的复杂性，上述方法在交通警力资源配置中仍面临一些挑战。首先，城市交通系统的动态性和不确定性使得模型难以准确捕捉到交通流的实际情况；其次，模型中需要考虑的因素众多，如交通流量、事故频发地点、交叉口状况等，如何合理权衡这些因素也是一个亟待解决的问题。
近年来，随着数据挖掘技术的成熟，学者开始利用大数据所隐含的时空特征优化警力配置。CHASE等[14]开发了一种混合整数线性优化公式来最小化响应时间失败的风险；LI Wenguang等[15]引入网格的概念和多机协作技术，利用无人机技术实时动态监控大场景、大区域，以此提高警用无人机在监控技术侦查中的检测效率；胡立伟等[16]构建随机森林朴素贝叶斯-耦合度模型研究了影响交通事故伤害程度的4类18个相关因素，为事故的预防提供了决策参考。为最大限度地利用有限的警力资源，挖掘警力资源的最大潜力，有必要借助海量的历史交通事故数据深入研究警力资源的优化配置[17-18]，使现有警力资源满足交通安全需求。
鉴于此，笔者拟利用车辆历史出行轨迹，提出城市路网的网格划分方法，并进一步结合历史交通事故数据集实现基于排队论模型的交通警力资源优化配置策略，通过对比试验论证该方法，以期为城市交通管理部门对警力资源的部署和调配提供有效的技术支撑。
1 交通警力资源配置问题建模
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交通警力资源优化配置的目的是在保证当事人等待时间不超过10 min的前提下，以最少的警员数量，完成对路网交通事故的处置任务。在此基础上，制定最佳的出警方案。
由于交警处理每一起事故都需要处置时间，并且只有处理完当前的事故后才能处理下一起事故。因此，在配备的交警人数有限的情况下，如果在短时间内发生的交通事故过载，交警无法及时处置时，待处理的事故被迫处于等待的状态。为使发生的交通事故与现场交警之间达到均衡，引入一个队列来存储无法及时处理的交通事故[19-20]。同时，对于交警处理实时发生的交通事故问题，把产生的交通事故看作数据的生产者，处理事故的交警看作数据的消费者。
为更好地求解问题，有必要对交通警力资源的分配问题进行一些潜在的约定，为所提基于排队论模型的警员配置方法提供数学基础。警力资源配置建模过程中涉及到的一些索引与参数见表1，约束条件见表2。
综上，将问题表述如下式：
m i n Z = ∑ i = 1 I Z ( S i ) s . t . T ( A c S i ， k ) + P ( L ， A j S i ) / v ¯ ≤ 1 / 6   L ∈ S i   C k S i ≤ 8 ， k ∈ N +   T ( M ) = 1 / 6 ， T ( C ) = 1 / 3
2 基于排队论的警力资源配置优化
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2.1 基于出行轨迹相似度的道路网格化管理
车辆的出行轨迹揭示了路段之间的时空相关性，并可作为路段之间相似度的一种考量。随着路网卡口系统的普及，获取车辆出行的完整轨迹成为可能。城市路网的卡口系统分布如图1所示。试验使用的车牌识别数据来自于城市交通重点实验室的实时监控视频，每条数据记录了包括设备编号、抓拍时间、车牌号以及车牌颜色在内的基本信息。通过路网卡口系统记录到的车牌数据每天可达到6 000多万条，数据量达到4GB，能够满足试验的数据需求和计算精度。
由于路网卡口系统捕获到的车牌识别数据中包含大量因客观原因所产生的粗差数据，因此，需要对原始数据进行预处理，去除那些明显的误差数据；再利用路网和卡口站点之间的空间位置关系和拓扑关系，进一步剔除车牌识别数据中的不合理记录。在此基础上，查询每一辆车单次出行所经过的卡口点位的集合，采用Dijkstra算法，计算点串中相邻2个点之间的路径，得到每一辆车完整的出行轨迹。
如果将路段集合 X ( x 1 ， x 2 ， … ， x n )中的每一条路段 x i视为空间中的一个点，使用无向带权图G(X，W)来描述整个路网数据集，其中，X表示原始路段数据集，W表示路段之间关联度的相似矩阵。采用文中方法得到某个时间段内所有车辆的轨迹集合，记为 R 1 ， R 2 ， … R p ， … ， R n，其中， R p = { r 1 ， r 2 ， … ， r m }表示第 p辆车的出行轨迹， r l ∈ R p表示在该出行轨迹中经过的第l个路段。定义任意2个路段之间的相关性为在所有出行轨迹的集合中2条路段被同时包含在一次出行轨迹中的次数。
求得第 h辆车的出行轨迹所贡献得到的路网相似度矩阵为 M h，N辆车的相似矩阵求和得到整个区域内路段的相似矩阵 W，如下式：
W = ∑ h = 1 N M h
W满足 W i j = W j i，对任意一路段 x i，定义该节点的度 d i为与其相连接的所有边的权重之和，即 d i = ∑ j = 1 n W i j，则求得度矩阵 D，如下式：
D = d 1   d 2     ⋱         d n
式中 d i为第i个节点的度。
定义拉普拉斯矩阵 L = D - W，归一化处理，得到矩阵 L 1 = D - 1 2 L D - 1 2。计算 L 1的特征值，并将特征值从小到大排序，得到特征值的集合 Γ = { λ 1 ， λ 2 ， … ， λ m }，取前 k个特征值组成新特征值集 Γ ' = { λ 1 ， λ 2 ， … ， λ k }，其中，每一个 λ i对应一个独立的特征向量 X i，为使后续的聚类效果更优，归一化处理每一个特征向量 X i得到特征向量 S i，而后即可建立特征向量集 H = S 1 ， S 2 ， … ， S k。将特征向量集 H中的 k个列向量组成特征矩阵 U = S 1 ， S 2 … ， S k，最后，使用k-means算法将样本 U进行聚类，得到城市道路网格化管理划分方案，如图2所示。
2.2 排队论模型求解
使用排队论模型求解各个网格中满足出警要求的最少警员数，使得在满足当事人最大等待时间的条件下，警员的执勤效率达到最高。假设交通事故发生的时间间隔服从参数 λ的负指数分布，安排s个交警负责处理指定网格内的交通事故，每个交警处理交通事故的时间包含从交警当前位置前往事故地点以及到达事故地点以后处理事故的时间，因此，认为服从参数μ的负指数分布[21-22]。当一起交通事故发生时，如果有空闲的交警，则马上前往事故地点进行处理，否则需要进入队列进行等待。假设 p n为到达平衡状态后队长N的概率分布，记 ρ s = ρ / s = λ / s μ ，其中， ρ = λ / μ表示系统中至少有一起交通事故的概率。当 ρ s < 1时，根据排队论模型，可得在平衡状态下发生的交通事故数为n的概率，如下式：
p n = ρ n n ! p 0 ， n = 1 ， 2 ， … ， s   ρ n s ! s n - s p 0 ， n ≥ s
其中， p 0 = ∑ n = 0 s - 1 ρ n n ! + ρ s s ! ( 1 - ρ s ) - 1。
当 n ≥ s，这时再发生交通事故就必须等待。由平稳分布可得平均排队长 E q为
E q = p 0 ρ s ρ s s ! ( 1 - ρ s ) 2
则平均队长 E s为
E s = E q + ρ
在平稳状态下，事故当事人的等待时间(等待交警赶到事故现场与等待处理的时间之和)的平均值为
z = c ' s s + c w E
式中：s为警员数量； c ' s为每一位交警处理事故产生的单位时间内的费用； c w为警员因处理每一起事故而产生停留的单位时间费用。由于 c ' s和 c w是给定的，唯一可变的是警员数量s，将z看成是s的函数，求使 z达到最小的 s *，有
E ( s * ) - E ( s * + 1 ) ≤ c ' s c w ≤ E ( s * - 1 ) - E ( s * )
当s=1，2，…，η时，依次求得E与相邻2个E值的差。根据 c ' s c w的值落在哪个与s相关的不等式中，即可定出最优的 s *。
综上，完整的算法流程如图3所示。
3 交通警力配置试验与分析
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为进一步验证排队论模型的有效性和优越性，对比试验网格划分方案下基于排队论模型的出警方案与传统“事故即发生即派遣警员”的出警方案，选取2021年3月4日07:00:00—09:00:00发生的历史交通事故作为样例数据。为使结果更加清晰直观，实际调查交警在路网中的平均行驶速度为50 km/h。通过基于排队论模型的事故处理方案，计算出在该时段内需要配置9名警员才能最有效地处理该区域内发生的交通事故。详细的出警方案见表3和图4a。
如果使用传统“事故即发生即派遣警员”的出警方案，交警在接到报警信息时，按照时间顺序依次前往各个事故点进行处理。为满足事故碰撞者等待警员到达事故现场的时间不超过10 min的限制，至少需要配置11位警员，与提出方法相比需要多投入18.18%的警力；同时，求解交警前往各个事故点的最优路径和所需的时间，见表3和图4b。对比2种警员配置策略，基于排队论模型的出警方案较传统方案降低10.87%的警员出行路程，同时，降低10.68%事故碰撞者的平均等待时间。
从图4中可以看出，传统的出警方案呈现出以交警中队为中心的辐射状分布，说明交通事故发生后，交警都将从中队出发前往事故现场进行事故处理，这造成警力资源的浪费和事故处置效率的下降；而基于排队论模型的警力资源配置方法能够克服这一弊端。排队论模型的引入让潜在的处于空闲状态的警员的执勤效率得到提升，从宏观上看，警员的出警线路呈现闭环状分布。为验证方法的泛化能力，将基于排队论模型的警力资源配置方法与传统方法应用到宁波市江北区的交通警力配置过程中，得到类似的结论，其出警方案的对比效果如图5所示。可见：基于排队论模型的交通警力资源优化配置方法可有效降低交通警察的人员投入数量，同时，也能够提升交警系统的响应速度和出警效率。
4 结论
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1) 提出一种基于出行轨迹相似度的路网划分方法，并应用于城市路网的网格化管理，助力交管部门有针对性的配置警力资源和采取预防措施。
2) 运用排队论模型对交通警力资源的配置问题进行建模，通过模型求解得出基于排队论模型的警力资源配置方法，能够减少18.18%的警员配置数量，提升了警员的配置效率。
3) 基于排队论模型的交通警员出警配置方案可进一步减少10.87%的出警巡航路程，并使事故处置的响应速度提高10.68%。
基金
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  • 浙江省哲学社会科学规划课题(22NDQN279YB)
  • 宁波市自然科学基金资助(2023J185)
文献
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2024年第34卷第7期
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doi: 10.16265/j.cnki.issn1003-3033.2024.07.0153
  • 接收时间：2024-01-15
  • 首发时间：2025-07-09
  • 出版时间：2024-07-28
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  • 收稿日期：2024-01-15
  • 修回日期：2024-04-16
基金
浙江省哲学社会科学规划课题(22NDQN279YB)
宁波市自然科学基金资助(2023J185)
作者信息
    1 宁波工程学院 网络空间安全学院，浙江 宁波 315211
    2 宁波市高等级公路建设管理中心，浙江 宁波 315199
    3 同济大学 交通运输工程学院，上海 201804
    4 兰州交通大学 交通运输学院，甘肃 兰州 730070
参考文献
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