﻿ 多股道城市轨道交通车站站前折返能力分析
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 同济大学学报(自然科学版)  2017, Vol. 45 Issue (9): 1328-1335.  DOI: 10.11908/j.issn.0253-374x.2017.09.011 0

### 引用本文

JIANG Zhibin, RAO Ya. Turnback Capacity Assessment at Rail Transit Stub-end Terminal with Multi-tracks[J]. Journal of Tongji University (Natural Science), 2017, 45(9): 1328-1335. DOI: 10.11908/j.issn.0253-374x.2017.09.011.

### 文章历史

Turnback Capacity Assessment at Rail Transit Stub-end Terminal with Multi-tracks
JIANG Zhibin, RAO Ya
Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China
Abstract: Turnback capacity becomes a major concern for the line capacity of rail transit. By taking a rail transit stub-end terminal with four-tail tracks as background, a mixed integer programming optimization model is formed based on N-track integrated model, to estimate the turnback capacity and the track occupation strategies with the objective of minimizing occupation times of trains. Operations and design parameters such as tail track allocation strategies, train layover time, homogeneity of trains are also considered in this model. We illustrate our model with computational experiments drawn from the real rail transit Line 16 in Shanghai and reach the results which show the track occupation strategy, maximum layover time and homogeneity impact on turnback capacity.
Key words: rail transit    terminal with crossovers located in advance of station    turnback capacity    layover time    homogeneity of trains

1 站前折返能力的影响因素分析

1.1 折返模式

 图 1 4线站前折返站的单股道折返示意图 Fig.1 Turnback operation of crossover located in advance of station with four tail tracks
1.2 停站时间

 图 2 出发等候时间的影响(单位：s) Fig.2 Influence of departure waiting time(Unit: s)
1.3 列车到发的均衡性

 图 3 到发均衡性对折返能力的影响(单位：s) Fig.3 Influence of turn-back capacity under the homogeneity of arrival or departure interval(Unit: s)
2 折返能力计算的整数规划模型 2.1 站前折返过程分析

 图 4 岛式站台四折返线站前折返示意图 Fig.4 Turn-back operation with crossover located in advance of four tail tracks station

 图 5 轨道选择和方向占用的拓扑结构 Fig.5 Topology diagram of events track occupation and direction of trains

 图 6 区段轨道列车区段运行占用顺序示意图 Fig.6 Topology diagram of track occupancy

(1) 同一轨道只能允许一列车占用；

(2) 对于连续的同方向列车占用同一轨道，需要错开同方向占用时间间隔；

(3) 对于连续的对向列车占用同一轨道，需要错开对向占用时间间隔.

2.2 模型建立

2.2.1 参数定义

2.2.2 目标函数

 ${\rm{Min}}\left( {{x_{{\rm{end,}}{l_{\rm{e}}}}} - {x_{{\rm{begin,}}{f_{\rm{e}}}}}} \right)$ (1)
2.2.3 约束条件

(1) 第一事件的开始事件与计算的开始时间相一致，有

 ${x_{{\rm{begin,}}{f_{\rm{e}}}}} = {t_{\rm{b}}}$ (2)

(2) 后一事件的开始时刻与前一事件的结束时刻必须保持一致，有

 ${x_{{\rm{begin,}}k + 1}} = {x_{{\rm{end,}}k}},\;\;\;k \notin {K_{{\rm{out,}}ij}},i \in U,j \in S$ (3)

(3) 车底按时间顺序进入车站进行折返作业，有

 ${x_{{\rm{begin,}}{f_{i + 1}}}} \ge {x_{{\rm{begin,}}{f_i}}},\;\;\;i \in U,i < {n_{{\rm{TU}}}}$ (4)

(4) 为保证先进先出，后一事件的结束时间必须大于前一事件的结束时间，有

 ${x_{{\rm{end,}}{l_{i + 1}}}} \ge {x_{{\rm{end,}}{l_i}}},\;\;\;i \in U,i < {n_{{\rm{TU}}}}$ (5)

(5) 在列车可以停留的区段上，列车的占用时间不小于该区段的最小占用时间，有

 $\begin{array}{*{20}{c}} {{x_{{\rm{end,}}k}} \ge {x_{{\rm{begin,}}k}} + {b_{k,j}}{d_{{\rm{in}},j,t}} + \left( {1 - {b_{k,j}}} \right){d_{{\rm{out,}}j,t}},}\\ {k \in K,j \in {S_{\rm{W}}},t \in {P_j}} \end{array}$ (6)

(6) 在不许等待或停留的区段内，事件的占用时间即为最小占用时间，有

 $\begin{array}{*{20}{c}} {{x_{{\rm{end,}}k}} = {x_{{\rm{begin,}}k}} + {b_{k,j}}{d_{{\rm{in}},j,t}} + \left( {1 - {b_{k,j}}} \right){d_{{\rm{out,}}j,t}},}\\ {k \in K,j \notin {S_{\rm{W}}},t \in {P_j}} \end{array}$ (7)

(1) 保证列车在每一区段必须并且只能占用一条轨道，有

 $\sum\limits_{t \in {P_j}} {{q_{k,t}}} = 1,\;\;\;k \in {K_{S,j}},j \in S$ (8)

(2) 进站列车必须从区段1的轨道A进入，有

 ${q_{k,1}} = 1,\;\;\;k \in {K_{{\rm{in,}}i,j}},i \in U,j \in {S_{\rm{T}}}$ (9)

(3) 出站列车必须从区段1轨道B离开，有

 ${q_{k,2}} = 1,\;\;\;k \in {K_{{\rm{out,}}i,j}},i \in U,j \in {S_{\rm{T}}}$ (10)

(4) 同一车底接续的列车占用的折返线必须保持一致，有

 $\begin{array}{*{20}{c}} {{q_{k,t}} = {q_{k - 1,t}}}\\ {k \in \left( {{K_{{\rm{in,}}i,j}} \cup {K_{{\rm{out,}}i,j}}} \right),t \in {P_j},i \in U}\\ {j \in {S_{\rm{P}}}} \end{array}$ (11)

(5) 如果列车选择轨道D进站，随后必须选择H，如果选择轨道C进站，随后必须选择G，即

 $\begin{array}{*{20}{c}} {{q_{k,t}} = {q_{k + 1,t}}}\\ {k \in {K_{{\rm{in,}}i,j}},i \in U,j \in {S_C},k < n{n_{TU}}} \end{array}$ (12)

(6) 如图 4所示，对于折返列车，若选择股道A，那么随后必须选择股道C或者D，若选择股道C，则随后必须选择股道F，若选择股道D，则随后必须选择股道G，若选择股道H或I为折返股道，那么随后必须选择轨道F进入道岔区间，若选择股道J或K为折返股道，那么随后必须选择轨道G进入道岔区间；对于选择F股道出站的列车，随后必须选择轨道D，对于选择G股道出站的列车，随后必须选择轨道E；对于选择轨道D或E的列车，随后必须选择轨道B出站，如

 $\begin{array}{*{20}{c}} {{q_{k,g}} = {q_{k - 1,1}}}\\ {k \in {K_{{\rm{in,}}i,j}},i \in U,j \in {S_{\rm{C}}},k < n{n_{TU}}}\\ {g = 1,2} \end{array}$ (13)
 $\begin{array}{*{20}{c}} {{q_{k,1}} = {q_{k - 1,1}}}\\ {k \in {K_{{\rm{in,}}i,j}},i \in U,j \in {S_{\rm{D}}},k < n{n_{TU}}} \end{array}$ (14)
 $\begin{array}{*{20}{c}} {{q_{k,2}} = {q_{k - 1,2}}}\\ {k \in {K_{{\rm{in,}}i,j}},i \in U,j \in {S_{\rm{D}}},k < n{n_{TU}}} \end{array}$ (15)
 $\begin{array}{*{20}{c}} {{q_{k,x}} = {q_{k + 1,1}}}\\ {k \in {K_{{\rm{out,}}i,j}},i \in U,j \in {S_P},k < n{n_{TU}}}\\ {x = 1,2} \end{array}$ (16)
 $\begin{array}{*{20}{c}} {{q_{k,y}} = {q_{k + 1,2}}}\\ {k \in {K_{{\rm{out,}}i,j}},i \in U,j \in {S_P},k < n{n_{TU}}}\\ {x = 3,4} \end{array}$ (17)
 $\begin{array}{*{20}{c}} {{q_{k,x}} = {q_{k + 1,z + 1}}}\\ {k \in {K_{{\rm{out,}}i,j}},i \in U,j \in {S_{\rm{D}}},k < n{n_{TU}}}\\ {z = 1,2} \end{array}$ (18)
 $\begin{array}{*{20}{c}} {{q_{k,m}} = {q_{k + 1,2}}}\\ {k \in {K_{{\rm{out,}}i,j}},i \in U,j \in {S_{\rm{C}}},k < n{n_{TU}}}\\ {m = 2,3} \end{array}$ (19)

(7) 如果两列车同时占用某一轨道，则需要判断是同向占用还是对向占用，然后选择对应的安全间隔时间来疏解，以保证安全，即

 $\begin{array}{*{20}{c}} {{x_{{\rm{begin,}}\hat k}} - {x_{{\rm{end,}}k}} \ge {h_{F,j,t}}{r_{k\hat k}} - M\left( {1 - {r_{k\hat k}}} \right)}\\ {k,\hat k \in {K_{S,j}},j \in S,k < \hat k - 1}\\ {{o_{\hat k}} = {o_k},{q_{k,t}} + {q_{\hat k,t}} = 2,t \in {P_j}} \end{array}$ (20)
 $\begin{array}{*{20}{c}} {{x_{{\rm{begin,}}\hat k}} - {x_{{\rm{end,}}k}} \ge {h_{{\rm{M}},j,t}}{r_{k\hat k}} - M\left( {1 - {r_{k\hat k}}} \right)}\\ {k,\hat k \in {K_{S,j}},j \in S,k < \hat k - 1}\\ {{o_{\hat k}} \ne {o_k},{q_{k,t}} + {q_{\hat k,t}} = 2,t \in {P_j}} \end{array}$ (21)
 $\begin{array}{*{20}{c}} {{x_{{\rm{begin,}}k}} - {x_{{\rm{end,}}\hat k}} \ge {h_{{\rm{M}},j,t}}\left( {1 - {r_{k\hat k}}} \right) - M{r_{k\hat k}}}\\ {k,\hat k \in {K_{S,j}},j \in S,k < \hat k - 1}\\ {{o_{\hat k}} \ne {o_k},{q_{k,t}} + {q_{\hat k,t}} = 2,t \in {P_j}} \end{array}$ (22)
 $\begin{array}{*{20}{c}} {{x_{{\rm{begin,}}k}} - {x_{{\rm{end,}}\hat k}} \ge {h_{F,j,t}}\left( {1 - {r_{k\hat k}}} \right) - M{r_{k\hat k}}}\\ {k,\hat k \in {K_{S,j}},j \in S,k < \hat k - 1}\\ {{o_{\hat k}} = {o_k},{q_{k,t}} + {q_{\hat k,t}} = 2,t \in {P_j}} \end{array}$ (23)

(1)4列车为一组循环折返

 $\begin{array}{*{20}{c}} {{x_{{\rm{begin,}}k + 5n}} - {x_{{\rm{begin,}}k + n}} = {x_{{\rm{begin,}}k + 4n}} - {x_{{\rm{begin,}}k}}}\\ {k \in K,k \le n\left( {{n_{{\rm{TU}}}} - 5} \right)} \end{array}$ (24)
 $\begin{array}{*{20}{c}} {{x_{{\rm{end,}}k + 5n}} - {x_{{\rm{end,}}k + n}} = {x_{{\rm{end,}}k + 4n}} - {x_{{\rm{end,}}k}}}\\ {k \in K,k \le n\left( {{n_{{\rm{TU}}}} - 5} \right)} \end{array}$ (25)

 $\begin{array}{*{20}{c}} {{q_{k + 4n,t}} = {q_{k,t}}}\\ {k \in K,k \le n\left( {{n_{{\rm{TU}}}} - 4} \right),}\\ {t \in {P_j},j \in S} \end{array}$ (26)

 $\begin{array}{*{20}{c}} {{x_{{\rm{end,}}k + 4n}} - {x_{{\rm{begin,}}k + 4n}} = {x_{{\rm{end,}}k}} - {x_{{\rm{begin,}}k}}}\\ {k \in K,k \le n\left( {{n_{{\rm{TU}}}} - 4} \right)} \end{array}$ (27)

(2) 均衡性约束

 $\begin{array}{*{20}{c}} {{x_{{\rm{begin,}}{f_{i + 2}}}} - {x_{{\rm{begin,}}{f_{i + 1}}}} = {x_{{\rm{begin,}}{f_{i + 1}}}} - {x_{{\rm{begin,}}{f_i}}}}\\ {i \in U,i < {n_{{\rm{TU}}}} - 1} \end{array}$ (28)
 $\begin{array}{*{20}{c}} {{x_{{\rm{end,}}{f_{i + 2}}}} - {x_{{\rm{end,}}{f_{i + 1}}}} = {x_{{\rm{end,}}{f_{i + 1}}}} - {x_{{\rm{end,}}{f_i}}}}\\ {i \in U,i < {n_{{\rm{TU}}}} - 1} \end{array}$ (29)
2.2.4 折返方案

(1) 固定站台轨道进行折返

 $\begin{array}{*{20}{c}} {{q_{k,t}} = 1}\\ {t \in {N_{{\rm{fix}}}},k \in {K_{S,j}},j \in {S_{\rm{P}}}} \end{array}$ (30)

(2) 固定2股道进行双线折返

 ${q_{k,1}} + {q_{k,2}} = 1\;\;\;k \in {K_{S,j}},j \in {S_{\rm{P}}}$ (31)

 ${q_{k,2}} + {q_{k,3}} = 1\;\;\;k \in {K_{S,j}},j \in {S_{\rm{P}}}$ (32)

 ${q_{k,3}} + {q_{k,4}} = 1\;\;\;k \in {K_{S,j}},j \in {S_{\rm{P}}}$ (33)
2.3 模型求解

3 案例分析

 图 7 上海轨道交通16号线滴水湖站车站配线图 Fig.7 Rack map of Dishuihu Station of Line 16 in Shanghai

3.1 方案设计

3.2 结果分析

 图 8 不同折返模式与不同停站时间条件下的折返间隔统计 Fig.8 Statistics of turn-back interval under different turn-back modes and different stopping time
3.2.1 不同折返模式下的能力分析

(1) 到发均衡性对折返能力的影响较大.在双线折返模式下，当停站时间小于140 s时, 均衡条件下的能力小于不均衡条件下的能力，而大于140s时，两种条件下的能力相同.在四线折返模式下，有相同的规律，但临界值为370 s.

(2) 四线折返模式下的能力不会小于双线交替折返模式下的能力，均衡条件下，当停站时间小于140 s时，能力相同，而大于140 s时，四线折返模式的能力要大于双线折返模式的能力.不均衡条件下，四线折返模式下的能力会一直大于双线折返模式下的能力.

3.2.2 不同停站时间下的能力分析

 图 9 不均衡间隔条件下的折返过程占用图(对应图 8的B点)(单位：s) Fig.9 Track occupation under the disproportion of arrival or departure interval (corresponding to Fig. 8-B)(Unit:s)
3.2.3 不同均衡条件下的能力分析

 图 10 均衡间隔、先到先发条件下的折返过程占用图(对应图 8-F点)(单位:s) Fig.10 Track occupation under the same arrival or departure interval and the rule of first in first out (Fig. 8-F)(Unit:s)
3.2.4 不同折返模式的适应性分析

(1) 在折返能力不紧张时，尽量采用单轨道折返或双线交替折返的模式；

(2) 在能力较为紧张的条件下，从车站组织作业过程的简化和车站客运组织的便利性出发，不均衡间隔条件下的双线折返模式最为适用；

(3) 在能力利用最为紧张时，且停站时间较长时，4线混合折返(尤其是不均衡)的折返模式更为适用.

4 结语

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