ADVANCES in NATURAL and APPLIED SCIENCES
ISSN: 1995-0772 Published BYAENSI Publication EISSN: 1998-1090 http://www.aensiweb.com/ANAS 2017 April 11(4): pages 388-394 Open Access Journal
A Bus Bridging Optimization Model for Single Point Operational Disruption of Urban Rail
Transit
Jianhui Sun, Hua Hu, and Zhigang Liu
College of Urban Rail Transportation,Shanghai University of Engineering Science Shanghai, China.
Received 28 February 2017; Accepted 22 March 2017; Available online 25 April 2017
Address For Correspondence: Jianhui Sun, College of Urban Rail Transportation,Shanghai University of Engineering Science Shanghai, China. E-mail: [email protected]
Copyright © 2017 by authors and American-Eurasian Network for ScientificInformation (AENSI Publication). This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/
ABSTRACT Rail transit is an important means of transport in the city,as a relatively closed, passenger-intensive network system, the event of long-term operational disruption not only will lead to the backlog of passenger flow in station, and will cause line-related order randomlyand passengers stranded, which will have a serious impact onnormal travel of passengers and the normal operation of the metro. How to provide the bridge service for the affected passengers from the existing bus stations or the first and last stations to the interrupted railway stations is the necessary means to improve the emergency management level and the service reliability of the urban public transport system. This paper mainly analyzes how to transfer the nearby public transportation in the time of the interruption of the rail transit operation and quickly evacuate the passenger flow at the interruption point and establish the optimization model of the bus connection.
KEYWORDS: Rail transit, Operational disruption, Bus bridging, Optimization model.
INTRODUCTION
Rail transit is an important part of urban public transport system, sharing most of the passenger flow in the city, which plays a decisive role in the smoothness of urban traffic. However, with the increasing mileage of rail transit operation, the probability of failure of rail transit equipment also increases, and almost can not be avoided. Once the rail transit in the process of running out of a sudden failure of operation, which will cause a large number of passengers stranded and cause serious impact.Therefore it is necessary and timely to Deploy buses from the near bus station and the buses are running a certain amount of public transport to the interruptional rail station to evacuate passenger, and It is necessary to establish an optimization model of bus connection under the disruption of rail transit operation. Many cities in China also increase the bus connection program in the rail transit emergency response system, which has been applied in practice. However, the current study and optimization of bus connections are still in a relatively basic stage, the bus connection is based on a relatively rough contingency plans and the existence experience to deal, there are many areas where can be optimized and improved.Abroad Kepaptsoglou[1], according to the layout of the bus network, will put minimizing the passenger travel time and the bus connection distance as the goal, through the design of the genetic algorithm to solve and select the final bridging route. Xiao Guan-yu[2] proposed a road network topology model, and established an optimal feasible path set model. Through combining the improved deletion algorithm[3] with the traditional one Diikst algorithm[4] to solve this model, so as to get the optimal path.TENG Jing[5] taking the fully play bus capacity and reduce operating costs, put forward designated area of responsibility for public transport in the rail transit network, and use this as a unit
ToCite ThisArticle: Jianhui Sun, Hua Hu and Zhigang Liu., A Bus Bridging Optimization Model for Single Point Operational Disruption of Urban Rail Transit. Advances in Natural and Applied Sciences. 11(4); Pages: 388-394
389 Jianhui Sun et al., 2017/Advances in Natural and Applied Sciences. 11(4) April 2017, Pages: 388-394 to allocate reasonably public transport vehicles and usethe scheduling program of the appropriate Level according to the extent of the impact of emergencies. The above research mainly focuses on the model optimization and algorithm solving of bus connection route, and less attention is paid to the dispatching and shuttle connection of emergency bus, and the optimization of the number of bus connections is not considered.Therefore, this paper establishes an optimization model for the bus connection of single station to the up and down adjacent reentry station, and designs an optimization algorithm to solve the problem of bus connection in the case of interruption of rail transit. I. DESCRIPTION OF BUS BRIDGING PROBLEM At present, large and medium-sized cities in China's public transport passenger flow is mainly undertaken by the rail transit and public transport, and rail transportation passenger flow is gradually increasing, showing the trend of the main rail transit supplemented by buses. Passenger flow characteristics of rail transport is a large flow, high density, concentrated and strong, rail transit trial operation stage or late stage of equipment instability, there is a possibility of single site or the full line operational interruption. In order to solve the transportation problem of the passenger stranded in the interruption of rail transit operation, this chapter will establish the optimization model of bus connection under the rail interruption. Bus connection refers to dispatch a certain amount of public transport vehicles to provide safe evacuation and alternative transport services for affected passengers several times between the interruption station and the normal operation station along the track line up and down the direction of operation from the nearby bus station or terminal station, as well as special emergency points during the operational interruption period of rail transit.This paper is mainly aimed at under the single-point rail transit operation interruption condition how to use the ground bus system to evacuate the passenger site.Bus connection diagram of single-point interruption is shown in figure 1.
Fig. 1: Bus bridging diagram of single-point interruption
The occurrence of unexpected events in the rail transit network is completely random, and the rail transit operators will formulate contingency plans for all kinds of specific emergencies, starting bus emergency linkage[1] when usually only happenthe event of a "larger" level rail traffic emergencies. In practice, starting the bus bridge transport when rail transit operations happen long-term interruption (such as operational interruption events for more than 30min), and taking the corresponding transport organization forms of the size of the track(normal section of the track operation) and bus short bridging (Rail operational interruption sections) to maintain the basic service level of the urban public transport system. It can be seen from Fig. 1 that the bus connection problem includes two processes, one is the emergency bus resource scheduling from the bus emergency interruption sending station and the interruption operation station,the other is the dredging path planning between the interruption operation station and the normal operation station of the emergency buses. Due to the limited resources of the emergency bus and the large number of passengers to be evacuated, usually emergency buses needs to be rounded up and down direction in order to complete the evacuation of all affected passengers. Therefore, the number of Circulatory transportation of the emergency bus vehicles should be optimized.
Model Establishment: A. Related variables and parameters a location of operation discontinued stations; Q（t） the number of stranded passengers at t time at the station, including two part passenger flow; u Q（t） the number of stranded passengers in the up direction; d Q（t）the number of stranded passengers in the down direction; Q（u t）、 Q（d t）Calculation formula as follows: u N（t） the number of buses from up direction adjacent station to the interrupted station;
390 Jianhui Sun et al., 2017/Advances in Natural and Applied Sciences. 11(4) April 2017, Pages: 388-394
N（d t） the number of buses from down direction adjacent station to the interrupted station; C standard passenger capacity of buses; full load coefficient of the buses.
N（j bus） the number of buses on the j Line in the City;
N（j bus） the number of emergency buses on the j Line in the City; u N（j bus ） the number of buses from up direction adjacent station to the interrupted station on the j line; d N（j bus ） the number of buses from down direction adjacent station to the interrupted station on the j line; u d Lbus Lj，Lj a set of all emergency bridging lines; u Lj the j emergency bridging line between the uplink adjacent station to the interrupted station; d Lj the j emergency bridging line between the downlink adjacent station to the interrupted station; N the maximum passenger capacity of the bus in j line; Cj
t(vj,v(a)) the shortest time from the j line to the operating interrupted station;
t(v（a1）,v(a)) the time from the operating interrupted station to uplink adjacent station;
t(v（a）,v(a1)) the time from the operating interruption station to downlink adjacent station. u Ta the total bridging time in up direction; d Ta the total bridging time in down direction;
Ta the total bridging time （area） the passenger attracting rate of the whole buses after the public vehicles of the part lines participating in bridging passengers; （area） the original attraction rate of bus passenger; the decreasing rate of attraction; （bus） the routes utilization rate of the whole buses after the public vehicles of the part lines participating in bridging passengers; （bus） the original utilization rate of bus routes; the decreasing rate of utilization; S the vector of the maximum number of emergency bridging vehicles on N lines; D the vector of the shortest distance from the bridging buses to the rail transit station on N lines;
Vs the bus speed; the time extension coefficient of the bus on the road; t . the shortest time from the bridging buses in n node to the rail transit station.; n B. Constraints Analysis The number of stranded passengers includes two part passenger flow: u d Q（t） Q（t） Q（t） (1) u u Q（t） N（t） C (2) d d Q（t） N（t） C (3)
The number of passengers stranded between the operation interruption site and the uplink adjacent station of the rail transit and between the operation interruption site and the upstream adjacent station of the rail transit is estimated in the model analysis stage. Suppose that the part of the uplink and downlink stranded passengers u shared by bus are Q and Qd . Only using the city's public vehicles resources of existing bus lines to transport B B emergently stranded passengers of rail transit station is clearly not enough, In other words, the city's public vehicle resources of existing lines only need to transport the part of the passengers as u u QB Q（t） (4)
391 Jianhui Sun et al., 2017/Advances in Natural and Applied Sciences. 11(4) April 2017, Pages: 388-394
d d QB Q（t） (5) （0,1） The passenger attracting rate of the whole buses after the public vehicles of the part lines participating in bridging passengers should meet the following constraints :
（area） （area） (6) （0,1） The routes utilization rate of the whole buses after the public vehicles of the part lines participating in bridging passengers should meet the following constraints:
（bus） （bus） (7) （0,1） The number of emergency bridging vehicles in the j line should satisfy the following constraints:
N（j bus） 1 (8) N（j bus）
In order to reduce the increasing of the stranded passengers, evidently dispatching the bus of the nearest public transport stop distance from the interruption site to bridge the stranded passengers and respectively evacuating passengers to the uplink and the downlink adjacent rail station, at the same time ,ensuring that the transport capacity of the bridging bus lines can not reduce significantly, so it needs to select the next close bus to bridge. Then the final bus emergency scheduling program should be to meet that the city bus passenger attraction and the decreasing extent of the bus route utilization are in acceptable range,and minimizing the total bridging time that need to share by buses`. Following the above objectives and constraints analyzed, and establishing optimized model to solve.
C. Objective Function Analysis: Supposing that the total number of passengers of all the bridging lines between the rail transit interruption site and the uplink adjacent station is (N（ bus u） N ), and between the rail transit interruption site and the j Cj j downlink adjacent station is (N（ busd） N ); The number of round trips of the buses can be obtained j Cj j according to the number of stranded passengers to be shared; the total bridging time of the up and down direction can be calculated separately according to the shortest transportation time in up and down direction,the longer time between the two determines the final passenger bridging completion time.The goal is to minimize this final passenger connection completion time, as follows:
MinT max Tu ,Td (9) a a a u u QB Ta 2 t(V（a 1）,V（a）) (10) (N(busu ) N ) j Cj j Qd d B (11) Ta 2 t(V（a）,V（a 1）) (N(busd ) N ) j Cj j
Model Solving: Step1:Construct an N-dimensional vector S （ N the total number of city bus lines), The valuesi N（j bus） of the i element in the vector represents the maximum number of emergency bridging vehicles on the j line.
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Step2:Construct an N-dimensional vector d （ N the total number of city bus lines ） ,The value di d(Vi,V(a)) of the i element in the vector s represents the shortest distance from the bridging buses to the rail transit station on the j line. Step3: The elements in the vector s are reordered in descending order by the size of the elements in the vector d, getting a new N-dimensional vectors,the distance between the corresponding bus lines of the first element and rail operational interruption station the shortest, the distance between the corresponding bus lines of the last element and rail operational interruption station the lonest. Step4: When the above constraints are satisfied, scheduling the vehicles of the j element of the corresponding lines of the vector to the rail operationl interruption station to bridge the stranded passenger in the upanddown line, When the number of bridging vehicles increase to a critical value that satisfies the constraint condition, the number of vehicles between the operational interruption site of the rail transit and the uplink N（bus u） adjacent stations reaches j ,and the number of vehicles between the operational interruption site of j the rail transit and the downlink adjacent stations reaches N（busd）. T max Tu ,Td of the target function j j value represents the bridging completed time of the rail transit stranded passengers. s (s ,s ,s , ,s ) (12) 1 2 3 N d (d ,d ,d , ,d ) (13) 1 2 3 N Then we can get the shortest time the shortest time from the bridging buses in n node to the rail transit station by Floyd algorithm[6] as
dN tn (14) Vs Final getting the total bridging time according to objective function.
Example Applications (Songjiang District of Shanghai): In this paper, the simulation analysis of the bus bridging in interruption conditionof Sheshan station of rail transit Line 9 in Songjiang District of Shanghai is carried out.Assuming that the number of trains between the Sheshan station and the uplink adjacent SiJing station is 1 and the number of trains between the Sheshan station and the downlink adjacent DongJing station is 1 during the interruption period,The standard number of passengers of every train is 350,and 6 trains per train.The full load coefficient of buses in the uplink and downlink directions is 1.3, and the number of passengers in the up and down directions are as follows:
u Q（t） 1 350 6 1.3 2730 (15) d Q（t） 1 350 6 1.3 2730 (16)
At the same time, it can get the number of the vehicles operating on lines according to the peak travel interval of every line in Songjiang District,; supposing the restriction coefficient of the exist number of vehicles in bus lines is 0.85, the number of emergency bridging vehicles of each line can be obtained according to the formula (8); The bridging time from starting point of each line to Sheshan station can be obtained from the time - distance matrix of road network in Songjiang district obtained according to Floyd algorithm, relevant data as follow table 1:
Table I: The bridging time(minutes) and the maximum number of bridging buses on each line from Songjiang to Sheshan Song Song Song Song Song Song Song Song Song Song Line name jiang Road jiang Road jiang Roadjiang jiang Road jiang jiang Roadjiang Road jiang jiang 92 55 56 Road 19 45 Road 46 47 13 Road 15 Road 16 Number of 4 4 4 2 8 4 6 8 8 6 vehicles Bridging 1 1 1 1 2 1 1 2 2 1 vehicles Bridging 0.6 5.5 5.5 8.9 14.0 14.0 14.0 16.1 16.1 16.1 time
Song Song Song Song Song Song Song Song Song Song jiang jiang Road jiang Road jiang Road jiang Road jiang Road jiang Road jiang Road jiang Road jiang Road Lines name Road 1 21 24 3 5 7 91 20 22 90 Number of 4 4 2 12 8 8 10 2 12 6
393 Jianhui Sun et al., 2017/Advances in Natural and Applied Sciences. 11(4) April 2017, Pages: 388-394
vehicles Bridging 1 1 1 2 2 2 2 1 2 1 vehicles Bridging 16.1 16.1 16.1 16.1 16.1 16.1 20.3 20.3 22.6 22.6 time
Song Song Song Song Song Song Lines name jiang Roadjiang Road jiang Road jiang Road jiang Road jiang Road
61 10 76 75 70 65 Number of 2 8 4 6 2 6 vehicles Bridging 1 2 1 1 1 1 vehicles Bridging 51.4 53.4 74.8 76.1 77.0 80.8 time
Supposing the stranded passengers ratio of SheShan station bridged by bus lines is 0.8, the bus bridging lines between Sheshan station to Si Jing station and the time getting Sheshan station can be obtained according to the bus bridging optimization model of the single station operating interruption and the corresponding solution method,thebridging times and the time as follow table 2; The bus bridging lines between Sheshan station to Dong Jing station and the time getting Sheshan station can be obtained as follow table 3.
Table II: The Bus Bridging Time From Sheshan to Si jing Song Song Song Song Song Song Song Song Song Song Song jiang jiang jiang jiang jiang jiang jiang jiang jiang Bridging lines jiang Road jiang Road Road Road Road Road Road Road Road Road Road 16 7 92 56 45 46 13 15 21 3 5 Getting station 0. 6 5.5 14.0 14.0 16.1 16.1 16.1 16.1 16.1 16.1 16.1 Bridging one time 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 Bridging two 20.3 20.3 20.3 0 0 0 0 0 0 0 0 times Song Song Song Song Song Song Song Song Song Song Shen jiang jiang jiang jiang jiang jiang Mei Min Zhong Bridging lines B Road Road Road Road Road Road line line line line 90 91 20 23 12 17
Getting station 20.3 20.3 22.6 22.6 24.4 24.4 24.4 24.4 24.4 24.8
Bridging one time 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3
Bridging two 0 0 0 0 0 0 0 0 0 0 times Songjiang 45 road determines the total bridging time in up line direction,the time is 54.6 minitesgetted from the table 2.
Table III: the bus bridging time from sheshan to dong jing Song Song Song Song Song Song Song Song Song Song Song jiang jiang jiang jiang jiang jiang jiang jiang Bridging lines jiang Road jiang Road jiang Road Road Road Road Road Road Road Road Road 19 1 7 55 45 47 13 15 24 3 5 Getting station 5.5 8.9 14.0 14.0 16.1 16.1 16.1 16.1 16.1 16.1 16.1 Bridging one time 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 Bridging two 11.1 11.1 11.1 0 0 0 0 0 0 0 0 times Song Song Song Song Song Song Song Song Song Song Shen Song jiang jiang jiang jiang jiang Mei Min Shen Bridging lines jiang Road B jiang Road Road Road Road Road Road line line line 20 line 6 90 22 25 17 18
Getting station 20.3 22.6 22.6 22.6 24.4 24.4 24.4 24.4 24.8 24.8 29.3 Bridging one time 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 Bridging two 0 0 0 0 0 0 0 0 0 0 0 times
Songjiang 6 road determines the total bridging time in down line direction,the time is 40.4minites getted from the table 3. So the time of bridging the Sheshan station stranded passengers to the uplink or downlink adjacent rail transit site needs 54.6 minites. The number of bridging buses of bridging routes of each line and the bus stopsis shown in Fig2, among which the red five-pointed star marks the operating disruption site Sheshan station and red circular marking the location of the bus stops where the bridging vehicles exist,and the number in the upper right corner indicates the number of bridging buses dispatched by the bus transfer stations, and the red solid line indicates the bridging route.
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Fig. 2: The bus bridging scheme of the stranded passengers in Sheshan station
Conclusion: It is a necessary means to improve the emergency management level and service reliability of urban public transit system by starting public transit bridging transportation in time under the long-time operation disruption of rail transit.This paper establishes an optimization model of bus bridging in single station operating interruption according to the possibility of operating interruption of single site or whole line,, which minimizes the completion time of passenger flow bridging in the interruption site of the rail as the objective function; According to the example of the public transit line network and the rail line network in Songjiang district, this paper by the Floyd algorithm gets the shortest path and time of bus vehicles between the interruptional station and the any node. The above model can be used to find the shortest time of bus bridging. The model provide a detailed bus bridging optimized program to evacuate timely the stranded passengers in condition of operating interruption of the rail. The operation and management personnel can dispatch the bus near the interruption station according to the number of the stranded passengers in the shortest time through the shortest route. However the paper only considers the interruption of single station operation of the rail transit, but do not consider the case of multiple sites at the same time interrupting. The number of stranded passengers at the site may be different from the assumed value. In addition, the bus bridging and auxiliary system is yet to be developed.
ACKNOWLEDGMENTS
The project is supported by the National Natural Science Foundation of China (Grant No.71601110) and the National Key Research and Development Plan of China (Grant No. 2016YFC0802505)
REFERENCES
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