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High-Speed Trains High-speed Passenger Trains on Freight Tracks: Modeling Issues on Capacity Analysis, Train Timetabling and Real-Time Dispatching Dr. Xuesong Zhou Assistant Professor Department of Civil and Environmental Engineering Univ. of Utah [email protected] In collaboration with Dr. Muhammad Babar Khan (Pakistan), Dr. Lingyun Meng (China) Prepared for NEXTRANS Seminar Series, Purdue University on May 11, 2010 Definitions High-speed passenger rail – 152 mph or faster for upgraded track – 183 mph or faster for new track In China, high-speed conventional rail lines operate at top speeds of 220 mph, and one maglev line reaches speeds of 270 mph. Reference: http://en.wikipedia.org/wiki/High-speed_rail High-Speed Trains E5 German designed third World speed generation ICEon Series Shinkan record holding Cologne-Frankfurt sen in Japan high-speed rail line (357mph) TGV First High-speed Service Train The Italian ETR 200 in 1939 It achieved the world mean speed record in 1939, reaching 127 mph near Milan The Acela Express, currently the only high-speed rail line in the U.S., with a top speed of 150 mph North American Railroad Network 5 major US railroads after years of consolidations: CSX, UP, CR, NS, BNSF (Planned) High-Speed Rail System in United States High-speed railway plans in China 17,000 mile national high-speed rail system will be built in 4 phases, for completion by 2030. Chicago Hub Network If implemented, the plans could return Chicago to a status it had in the 1930s and 1940s •France has a population distribution similar to that in the Midwest. •French experiences with TGV trains and other high-speed systems could conceivably be duplicated in the U.S. • The total cost was projected at $68.5 billion in 2009 dollars, • Only 54% was projected to need public financing if a public-private partnership was pursued. •The public funds could be recovered from revenues in about 15 years. Reference: http://en.wikipedia.org/wiki/Chicago_Hub_Network http://www.midwesthsr.org/docs/SNCF_Midwest.pdf Operational High-Speed Lines in Europe High-Speed Lines in East Asia Concepts of the two modes Operation Mode I (Dedicated Line) Operation Mode II (High-speed passenger trains running on freight tracks) + What We Need to Do in United States? 1. Building Infrastructure – Class I Railroad mileage shrank from 210K to 94K, from 1956 to 2007 – Railroad ton-miles tripled from 589 billion to 1.772 trillion (thanks to technological advance) 2. Building Education Infrastructure for Railroad Transportation Engineering Employment dropped from 1 million to 167K 3. Building New Tracks for Research… Reference: Barkan, C.P.L. 2008. Building an Education Infrastructure for Railway Transportation Engineering: Renewed Partnerships on New Tracks, TR News 257: 18-23, Transportation Research Board of the National Academies, Washington, DC. Railroad Planning and Operations Socio-economic data, Traffic OD Demand interview samples Estimation Traffic OD Demand Matrix Infrastructure Service Network Resources Design Yard and Terminal (yards and terminals) Blocking Management Line Plan Plan Route and Frequency Settings Train Scheduling TrainTrain Dispatching Dispatching, empty Train Timetables Emptycar Cardistribution Distribution Resources and Locomotive, Car and Crew Policies Scheduling Railroad Network Capacity Line capacity – Single or double-track -> meet-pass plans – Signal control type -> minimal headways – Locomotive power -> speed, acceleration/deceleration time loss – Train schedules -> overall throughput Node capacity (yards, terminals / sidings) – Track configuration – Locomotive power-> car processing time – Yard make-up plans, terminal operating plans -> overall throughput OD Demand -> Routes-> Blocks-> Trains destination origin b c d a 100 100 500 b 150 200 c 50 a b c d b a d Candidate blocks c b a d Blocking Plan 1 Train schedule Da c + Da d Dad+Dbd Time Dab+Dac+Dad d + Db c + Db d + Dc d c b c Blocking Plan 2 a d Da d Dab+Dac Da c + Db c + Db d Db d + Dc d Terminals c b Station Block a Background on Train Scheduling Important role in railroad management: Determine the level-of-service of train timetables Serve as the basis for locomotive and crew scheduling Planning Applications Real-time Applications – Satisfy passenger and Adjust the daily and hourly train freight traffic demand operation schedules – Minimize the overall – Improve on-time performance operational costs and reliability Demand Rolling stock Crew Line Planning Timetabling estimation scheduling scheduling Railway Planning Process Sequential scheduling – Stage 1: Line planning – Determine the routes, frequencies, preferred departure times, and stop schedules – Stage 2: Schedule generation . Construct the arrival and departure times for each train at passing stations . Job-shop scheduling formulation and branch-and-bound solution algorithm (Szpigel, 1973) » Minimize a weighted sum of train delays (Kraft, 1987) . Multi-criteria scheduling (e.g. Higgins and Kozan, 1998) » Mainly focus on the supply side, such as fuel costs for locomotives, labor costs for crews » Simplify multiple objectives as a weighted linear combination Train Scheduling on Beijing-Shanghai High-Speed Passenger Railroad in China Around 900 miles High-speed trains (200 mile/h) – Provide direct service for inter- city travel in this corridor Medium-speed trains (150 mile/h) – Run on both high-speed line and adjacent regular rail lines in order to . Serve the large volume of traffic passing through this corridor Reduce connecting delay for interline travel Illustration From Shanghai to Xuzhou 17 segments, 385 miles Morning period (6:00 am- 12:00 am) 24 high-speed trains and 12 medium-speed trains Preferred departure time interval for high-speed trains is 30 minutes Part I: Balancing Two Conflicting Objectives Two conflicting objectives – (High-speed trains) Expect a “perfect” schedule with high frequency and even departure time intervals – (Medium-speed trains) Reduce total travel time Operational policies – High-speed trains hold higher priority, i.e. medium-speed trains have to yield to high-speed trains, if possible conflict exists – A “perfect” high-speed train timetable might result in extremely long waiting times for medium-speed trains Need for – Obtain non-dominated solutions for bicriteria scheduling problem – Retrieve the trade-offs between two conflicting objectives Reference: Zhou, X. and Zhong, M. (2005) Bicriteria Train Scheduling for High- Speed Passenger Railroad Planning Applications. European Journal of Operational Research Vol 167/3 pp.752-771. Challenge I Challenge II: Model Acceleration and Deceleration Time Losses Acceleration and deceleration time losses . High-speed trains: 3 minutes . Medium-speed trains: 2 minutes Time axis station k+1 p p d q(i), k-1 q(i), k-1 τ q(i),k −1 section k station k section k-1 a τ q(i),k pq(i), k p station k-1 q(i), k bypass station k stop at station k Formulating Train Timetabling and Dispatching Problem Given – Line track configuration – Minimum segment and station headways – # of trains and their arrival times at origin stations Find – Timetable: Arrival and departure times of each train at each station Objectives – (Planning) Minimize the transit times and overall operational costs, performance and reliability – (Dispatching) Minimize the deviation between actual schedules and planned schedule Notations i: subscript of trains j: subscript of sections u: train types , 0: high-speed train, 1: medium-speed train pu,k : pure running time for train type u at section k without acceleration and deceleration times a τ u,k : acceleration time loss at the upstream station of section k with respect to train type u d τ u,k : deceleration time loss at the downstream station of section k with respect to train type u e l h u,v,k h u,v,k : minimum headway between train types u and v entering/leaving section k s i,k : scheduled minimum stop time for train i at station k ~ d : preferred departure time for train i at its origin, i.e. the preferred i release time for job i. Decision Variables di : departure time for train i at its origin yi : interdeparture time between train i and train i+1 e : entering time for train i to section k xi,k l : leaving time for train i from section k xi,k t a : actual acceleration time for train i at the upstream station of i,k section k d ti,k : actual deceleration time for train i at the downstream station of section k : total travel time for train i Ci Bi, j,k : 0 or 1, indicating if train i enters section k earlier or later than train j, respectively a Bi,k : 0 or 1, indicating if train i bypasses/stops at the upstream station of section k, respectively d Bi,k : 0 or 1, indicating if train i bypasses/stops at the downstream station of section k, respectively Model Acceleration and Deceleration Time Losses Multi-mode resource constrained project scheduling approach Activity (i, k) :the process of train i traveling section k and the project is a sequence of K activities Two sets of renewable resources are entering times and leaving times for each section the minimum headway constraints define the consumption of resources by each activity Processing time of activity (i, k) with train type u=q(i) in mode m (0=no-stop and 1=stop) l l pt(q(j),m,k) h q(j),q(i), k h q(i),q(j), k Time axis station k+1 pu,k if m = 00 xl l i,k x j,k d section k p +τ u,k if m = 01 e e u,k x i,k x = j,k pt(u,m,k) a station k pu,k +τ u,k if m = 10 l x j,k-1 a d section k-1 pu,k +τ u,k +τ u,k if m = 11 he e q(j),q(i), k h q(i),q(j), k Apply the algorithm proposed by Patterson et al.
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