Non-Periodic Train Line Planning for a Rail Network: Passenger Demand Responsive in Term of Time Distribution

Non-Periodic Train Line Planning for a Rail Network: Passenger Demand Responsive in Term of Time Distribution Huiling Fu, Ph.D. School of Traffic 聂磊 and Transportation Beijing Jiaotong University, PR. China A joint work with Wencheng Huang March 24th, 2015

Outline Motivation and Aim Proposing Approach Algorithm Case Study Conclusions and Future Works 2

Outline Motivation and Aim Proposing Approach Algorithm Case Study Conclusions and Future Works 3

Motivation and Aim Rail companies always pursue Frequent regular train service Transfer free train connections Fast and convenient transfer train connections Line Planning Timetabling 4

Motivation and Aim Routes Line Planning Stops Train capacity Frequency Departure times Arrival times Timetabling 5

Motivation and Aim Periodic Line Plan and Timetable 6

Motivation and Aim Non-periodic Line Plan and Timetable 7

Motivation and Aim Periodic Line Plan One hour plan Timetable Line Plan Timetable Non-periodic One day plan 8

Motivation and Aim Line Plan Timetable Non-periodic Challenge: determine the train paths sequence of a whole day 9

Motivation and Aim The aim of this research According to the time distribution of passenger demand among multiple ODs Line Plan Allocating each train line a departure time Non-periodic Timetable 10

Outline Motivation and Aim Proposing Approach Algorithm Case Study Conclusions and Future Works 11

Proposing Approach To estimate each train line a departure time: Maximize the amount of passengers whose expected departure times can be satisfied Linear integer programming Input: a given line plan, the total amount of forecasted passenger demand among each OD and its time distribution in each hour period Output: variables of passenger flow, and departure time of each train 12

Proposing Approach The model each train has its served passengers expected departure times to be met to the maximum extent 13

Proposing Approach The model Passenger flow assigned on a train should not exceed the seating capacity Passenger flow conservation 14

Proposing Approach The model Intervals between two departure/arrival trains at a station 15

Proposing Approach The model Headways between train paths 16

Proposing Approach The model Assure a train runs within permitted operating time period 17

Outline Motivation and Aim Proposing Approach Algorithm Case Study Conclusions and Future Works 18

Algorithm Descriptive: Two types of decision variables sometimes do not interact directly Disaggregate passenger flow assigning process Each passenger now has a departure time preference 19

Algorithm Integrated Algorithm Procedure Step 1: Preprocess the super long-distance trains Step 2: Select a set of train paths for passengers of one OD pair Step 3: Determine the departure times (sequence) of trains Step 4: Judge when the algorithm ends 20

Algorithm Integrated Algorithm Procedure Step 1: Preprocess the super long-distance trains Step 2: Select a set of train paths for passengers of one OD pair Step 3: Determine the departure times (sequence) of trains To match the distance of selected trains with long-distance; large volume; Step 4: Judge when the algorithm ends the passenger trip distance. major stations. 21

Algorithm Integrated Algorithm Procedure Step 1: Preprocess the super long-distance trains Step 2: Select a set of train paths for passengers of one OD pair The comparison-ofpair sorting idea A weight: ratio between passenger and train traveling distance Step 3: Determine the departure times (sequence) of trains Step 4: Judge when the algorithm ends Minimizing the passengers total travel times 22

Outline Motivation and Aim Proposing Approach Algorithm Case Study Conclusions and Future Works 23

Case Study Harbin West Shenyang North Langfang Tianjin South Dalian Cangzhou West Dezhou East Qingdao Jinan Zaozhuang Xuzhou East Suzhou East Bengbu South Chuzhou Nanjing South Zhenjiang South Changzhou North Wuxi East Suzhou North Shanghai Hongqiao Beijing South Shijiazhuang Taiyuan South Higher-classified stations Lower-classified stations Jinan West Taian Zhengzhou East Xian North Hefei Wuhan Xin Chongqing Chengdu East Changsha South Hangzhou East Guangzhou South Nanchang West Fuzhou South 24

Case Study BJ S LF TJ S CZ W DZ E JN W TA ZZ XZ E SZ E BB S CZ S NJ S ZJ W CZ N WX E SZ N SH HQ HB W DL 7 13 4 HB W 2 SY N 1 QD QD QD 9 5 6 11 5 HZ E 2 HZ E 6 HZ E, FZ S 5 QD 6 1 QD 3 HF 2 CS S 2 WH, CS S, GZ S QD 3 XA N 1 ZZ E, XA N 6 X CQ CD E HF 2 4 2 WH, HF 3 X CQ, WH 4 7 4 2 2 1 2 7 SY N 2 QD HB W 1 QD 2 1 TY S 1 QD 1 QD 1 1 Higher-classified stations 1 GZ S 7 Lower-classified stations HF 1 HF 2 2 2 8 6 3 4 NC W FZ S HZ E HZ E HZ E FZ S HZ E HZ E HZ E HZ E FZ S 51 types of trains 237 OD pairs 18 hours 25

Case Study Demand aspect: Passenger demand distribution Hourly passenger demand distribution can be derived from available historical ticket data Correction We issued over 570 questionnaires at six stations 26

Case Study More passengers are willing to start trips at the time later than the time when the trains depart in the morning Hourly demand distribution of short-distance passengers 27

Case Study Results: 28

Case Study Part solution of departure times (sequence) of trains Train No. Departure time Arrival time Departure station Destination station Intermediate stopping station(s) Travel distance (km) G1 6:39 8:12 BJ S JN W 3 406 G3 6:45 7:48 NJ S HZ E 18 256 G5 6:56 8:38 HF SH HQ 13 449 G7 6:57 8:51 BJ S JN W 2-3-4-5 406 G9 7:00 16:53 HB W HZ E 1-3-6-9-13-18 2,730 G11 7:00 15:14 DL HZ E 1-3-6-9-13-18 2,235 G13 7:00 13:44 BJ S FZ S 19 2,011 G15 7:00 13:51 TJ S FZ S 6-9-13-18 1,889 G17 7:00 14:00 JN W GZ S 25-24 2,005 G19 7:00 13:56 X CQ SH HQ 13 2,021 G21 7:00 11:44 SY N QD 1 1,370 G23 7:00 12:30 QD HZ E 6-9-13-18 1,484 G25 7:05 13:46 HB W QD 1-3 1,908 G27 7:05 14:01 X CQ SH HQ 25 2,021 G29 7:05 11:41 BJ S SH HQ 3 1,318 G31 7:10 14:12 HB W QD 1-2-3-4-5 1,908 G33 7:10 14:24 JN W GZ S 7-8-9-11 2,005 G35 7:10 11:46 BJ S SH HQ 9 1,318 G37 7:15 11:51 BJ S SH HQ 13 1,318 G39 7:15 11:15 JN W HZ E 9-13-18 1,071 G41 7:20 16:01 CD E FZ S 13-18 2,508 G43 7:25 11:02 BJ S NJ S 3 1,023 29

Case Study The number of passengers whose expected departure times are not satisfied The number of passengers with their desirable departure times fully met Realized departure time for demand of time section k from station i to j Expected departure time for demand of time section k^ from station i to j 30

Case Study The number of passengers whose expected departure times are not satisfied The number of passengers with their desirable departure times fully met Realized departure time for demand of time section k from station i to j Expected departure time for demand of time section k^ from station i to j 31

Case Study Satisfaction of expected departure times of passengers Passenger OD Passenger volume Unsatisfied passengers δ (people/d) (people/d) HB W-HZ E 595 21 4.758 10-3 BJ S-SH HQ 9,540 102 1.005 10-3 JN W-SH HQ 1,858 33 2.712 10-4 HF-SH HQ 2,508 48 4.878 10-4 Passenger OD Passenger volume (people/d) Unsatisfied passengers (people/d) δ (not meet the criterion) LF-DZ E 241 147 2.085 TJ S-ZZ 166 88 0.651 ZZ-CZ S 11 11 JN W-ZJ S 51 40 0.490 TJ S-CZN 89 60 0.828 CZ W-TA 107 87 2.447 DZ E-ZZ 133 73 0.904 32

Case Study Part solution of departure times (sequence) of trains Train No. Departure time Arrival time Departure station Destination station Intermediate stopping station(s) Travel distance (km) G1 6:39 8:12 BJ S JN W 3 406 G3 6:45 7:48 NJ S HZ E 18 256 G5 6:56 8:38 HF SH HQ 13 449 G7 6:57 8:51 BJ S JN W 2-3-4-5 406 G9 7:00 16:53 HB W HZ E 1-3-6-9-13-18 2,730 G11 7:00 15:14 DL HZ E 1-3-6-9-13-18 2,235 G13 7:00 13:44 BJ S FZ S 19 2,011 G15 7:00 13:51 A rough TJ S scheme FZ S 6-9-13-18! 1,889 G17 7:00 14:00 JN W GZ S 25-24 2,005 G19 7:00 13:56 X CQ SH HQ 13 2,021 G21 7:00 11:44 SY N QD 1 1,370 G23 7:00 12:30 QD HZ E 6-9-13-18 1,484 G25 7:05 13:46 HB W QD 1-3 1,908 G27 7:05 14:01 X CQ SH HQ 25 2,021 G29 7:05 11:41 BJ S SH HQ 3 1,318 G31 7:10 14:12 HB W QD 1-2-3-4-5 1,908 G33 7:10 14:24 JN W GZ S 7-8-9-11 2,005 G35 7:10 11:46 BJ S SH HQ 9 1,318 G37 7:15 11:51 BJ S SH HQ 13 1,318 G39 7:15 11:15 JN W HZ E 9-13-18 1,071 G41 7:20 16:01 CD E FZ S 13-18 2,508 G43 7:25 11:02 BJ S NJ S 3 1,023 33

Case Study 34

Case Study Satisfaction of expected departure times of passengers Passenger OD Passenger volume Unsatisfied passengers δ (people/d) (people/d) HB W-HZ E 595 21 4.758 10-3 BJ S-SH HQ 9,540 102 1.005 10-3 JN W-SH HQ 1,858 33 2.712 10-4 HF-SH HQ 2,508 48 4.878 10-4 Passenger OD Passenger volume (people/d) Unsatisfied passengers (people/d) δ (not meet the criterion) LF-DZ E 241 147 2.085 TJ S-ZZ 166 88 0.651 ZZ-CZ S 11 11 JN W-ZJ S 51 40 0.490 TJ S-CZN 89 60 0.828 CZ W-TA 107 87 2.447 DZ E-ZZ 133 73 0.904 35

Case Study Slows down the average train travel speed Brings more train operation cost Passenger OD Passenger volume (people/d) Unsatisfied passengers (people/d) LF-DZ E 241 47 TJ S-ZZ 166 16 ZZ-CZ S 11 0 Improved by JN W-ZJ S 51 0 adjusting train stops TJ S-CZN 89 0 CZ W-TA 107 7 DZ E-ZZ 133 33 δ 1.203 10-3 2.358 10-3 0 0 0 2.477 10-4 5.122 10-4 36

Outline Motivation and Aim Proposing Approach Algorithm Case Study Conclusions and Future Works 37

Conclusions and Future Works Conclusions: The paper proposes a model seeking to allocate each train line a departure time A heuristic has been adapted to the model The heuristic provides good solutions to the objective of maximizing passenger satisfaction Future works: Collaboratively optimize train schedule 38