地铁应急救援车辆配置绩效评估模型

张勇; 伏紫妍

doi:10.19818/j.cnki.1671-1637.2019.02.014

地铁应急救援车辆配置绩效评估模型

doi: 10.19818/j.cnki.1671-1637.2019.02.014

张勇^1,,
伏紫妍^2, ,

1.
苏州大学轨道交通学院, 江苏苏州 215131
2.
苏州工业园区测绘地理信息有限公司, 江苏苏州 215027

基金项目:

国家自然科学基金项目 51778386

国家社科基金重大项目 13 & ZD175

详细信息

作者简介:
张勇(1978-), 男, 江苏如东人, 苏州大学副教授, 工学博士, 从事交通可靠性及紧急救援研究

通讯作者:
伏紫妍(1993-), 女, 江苏扬州人, 苏州工业园区测绘地理信息有限公司工程师

中图分类号: U298.6
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出版历程
- 收稿日期: 2018-09-05
- 刊出日期: 2019-04-25

Evaluating model of deployment performance of metro emergency rescue vehicles

ZHANG Yong^1
,,
FU Zi-yan^{2
, ,}

1.
School of Rail Transportation, Soochow University, Suzhou 215131, Jiangsu, China
2.
Suzhou Industrial Park Surveying, Mapping and Geoinformation Co., Ltd., Suzhou 215027, Jiangsu, China

More Information

Author Bio:
ZHANG Yong (1978-), male, associate professor, PhD, sinkey@126.com

FU Zi-yan (1993-), female, engineer, 1542533384@qq.com

摘要

摘要: 分析了地铁应急救援车辆对地铁灾害事故实施救援的排队过程, 定义了救援车辆响应地铁灾害事故的状态空间, 基于随机生灭过程理论建立了救援车辆的联合排队模型, 得到救援状态平衡方程; 为了减小平衡方程求解的运算量与存储空间, 提出了基于稀疏矩阵压缩的联合排队状态概率改进求解算法, 给出了包括救援响应时间、救援车辆工作强度、跨区救援概率等地铁救援系统各项绩效评价指标计算方法; 为了验证模型与求解算法, 以实际的地铁线网为例, 研究了路轨两用救援车、履带式救援车和便携式救援车的性能指标。计算结果表明: 算法迭代7次以后, 收敛精度数量级达到了10^-8; 路轨两用救援车、履带式救援车和便携式救援车的平均响应时间分别约为14、20、10 min; 路轨两用救援车、履带式救援车跨区救援概率分别约为0.85、0.75, 便携式救援车跨区救援概率数量级为10^-5; 在各小区接收外部救援车方面, 路轨两用救援车和履带式救援车跨区救援概率约为0.7, 而便携式救援车跨区救援概率的数量级约为10^-6; 在救援强度的均衡性方面, 路轨两用救援车、履带式救援车和便携式救援车依次降低。
- 地铁应急救援 /
- 联合排队模型 /
- 救援概率 /
- 救援车辆配置 /
- 便携式救援车
Abstract: The rescue operation queue process of metro emergency rescue vehicles (MERVs) responding to metro disasters was analyzed. By defining the state space of MERVs in response to metro disasters, the joint queuing model of MERVs' rescue states was established based on the random birth-death process theory and obtained balance equations. In order to reduce the computation amount and storage space of balance equations, an improved solving algorithm of joint queuing state probability based on the sparse matrix compression was developed. The calculation methods of various performance evaluation indexes of metro rescue system, including the rescue response time, MERVs working intensity and cross-district rescue probability, were given. In order to verify the model and algorithm, the actual metro network was taken as an example, and the performance indexes of three types of MERVs, including the road-rail rescue vehicle, crawler rescue vehicle and portable rescue vehicle, were studied. Calculation result shows that the magnitude of convergence precision reaches 10^-8 after the algorithm iterates 7 times. The average response times of road-rail rescue vehicle, crawler rescue vehicle and portable rescue vehicle are about 14, 20 and 10 min, respectively. The cross-district rescue probabilities of road-rail rescue vehicle and crawler rescue vehicle are about 0.85 and 0.75, respectively, and the magnitude of portable rescue vehicle is 10^-5. For the regions receiving external rescues, the rescue probabilities of road-rail rescue vehicle and crawler rescue vehicle both are about 0.7, while the magnitude of portable rescue vehicle is about 10^-6. For the balance of rescue intensity, they are sequentially decline the road-rail rescue vehicle, crawler rescue vehicle and portable rescue vehicle.
- metro emergency rescue /
- joint queuing model /
- rescue probability /
- deployment of rescue vehicle /
- portable rescue vehicle

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图 1 路轨两用救援车分布

Figure 1. Deployment of road-rail rescue vehicles

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图 2 应急救援车辆空间分布

Figure 2. Deployment of emergency rescue vehicles

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图 3 三辆救援车辆的救援状态转移

Figure 3. Transitions between rescue states of 3 rescue vehicles

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图 4 算法流程

Figure 4. Algorithm flow

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图 5 地铁线网与救援小区

Figure 5. Railway network and rescue zones

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图 6 状态概率精度迭代收敛曲线

Figure 6. Iterative convergence curve of state probability precision

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图 7 救援车辆平均响应时间

Figure 7. Mean response times of rescue vehicles

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图 8 救援车辆工作强度

Figure 8. Workloads of rescue vehicles

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图 9 路轨两用救援车与履带式救援车跨小区救援概率

Figure 9. Cross-district rescue probabilities of road-rail rescue vehicles and crawler rescue vehicles

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图 10 便携式救援车跨小区救援概率

Figure 10. Cross-district rescue probabilities of portable rescue vehicles

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图 11 各小区利用路轨两用救援车与履带式救援车获得救援的概率

Figure 11. Rescue probabilities of each zone obtained by using road-rail rescue vehicles and crawler rescue vehicles

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图 12 各小区利用便携式救援车获得救援的概率

Figure 12. Rescue probability of each zone obtained by using portable rescue vehicles

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表 1 救援车辆配置

Table 1. Deployment of rescue vehicles veh

线路	小区	车型数量
线路	小区	路轨两用救援车	履带式救援车	便携式救援车
1号线	1	0	2	1
	2	0	0	2
	3	0	0	3
	4	0	0	2
	5	1	2	2
5号线	6	0	2	2
	7	0	0	2
	8	0	0	3
	9	0	0	2
	10	1	2	1

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表 2 2007~2014年北京市地铁救援次数与时间

Table 2. Railway rescue times and time of Beijing during 2007-2014

年份	每年救援次数		平均救援时间/min
年份	1号线	5号线	平均救援时间/min
2007	2	2	23.0
2008	2	1	24.7
2009	2	1	47.5
2010	2	1	30.0
2011	3	0	16.3
2012	2	0	18.8
2013	0	2	20.0
2014	5	2	13.8

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表 3 路轨两用救援车和履带式救援车在小区间的行程时间

Table 3. Travel times of road-rail rescue vehicles and crawler rescue vehicles between zones h

小区	1	2	3	4	5	6	7	8	9	10
1	0.08	0.18	0.34	0.48	0.61	0.99	1.14	1.29	1.14	1.02
2	0.18	0.10	0.17	0.30	0.44	0.99	1.14	1.46	1.31	1.20
3	0.34	0.17	0.07	0.14	0.27	0.82	0.97	1.27	1.24	1.13
4	0.48	0.30	0.14	0.06	0.13	0.69	0.84	1.13	1.11	1.00
5	0.61	0.44	0.27	0.13	0.07	0.55	0.70	1.00	0.98	0.86
6	0.99	0.99	0.82	0.69	0.55	0.08	0.15	0.23	0.45	0.56
7	1.14	1.14	0.97	0.84	0.70	0.15	0.07	0.15	0.30	0.41
8	1.29	1.46	1.27	1.13	1.00	0.23	0.15	0.08	0.15	0.19
9	1.14	1.31	1.24	1.11	0.98	0.45	0.30	0.15	0.07	0.11
10	1.02	1.20	1.13	1.00	0.86	0.56	0.41	0.19	0.11	0.04

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表 4 便携式救援车在小区间的行程时间

Table 4. Travel times of portable rescue vehicles between zones h

小区	1	2	3	4	5	6	7	8	9	10
1	0.19	0.44	0.86	1.19	1.53	0.99	1.14	1.29	1.14	1.02
2	0.44	0.24	0.42	0.76	1.09	0.99	1.14	1.46	1.31	1.20
3	0.86	0.42	0.18	0.34	0.67	0.82	0.97	1.27	1.24	1.13
4	1.19	0.76	0.34	0.16	0.33	0.69	0.84	1.13	1.11	1.00
5	1.53	1.09	0.67	0.33	0.18	0.55	0.70	1.00	0.98	0.86
6	0.99	0.99	0.82	0.69	0.55	0.21	0.38	0.58	1.12	1.40
7	1.14	1.14	0.97	0.84	0.70	0.38	0.17	0.37	0.74	1.03
8	1.29	1.46	1.27	1.13	1.00	0.58	0.37	0.20	0.38	0.48
9	1.14	1.31	1.24	1.11	0.98	1.12	0.74	0.38	0.18	0.28
10	1.02	1.20	1.13	1.00	0.86	1.40	1.03	0.48	0.28	0.11

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