q/.r NSRZKLA4-P1 Capacity planning for railway systems Leo Kroon Jan 17, 2002

q/.r NSRZKLA4-P2 Conclusions Capacity planning at several levels Relevant resources are: ¶ Infrastructure ¶ Rolling stock ¶ Personnel ¶... All relevant resources are scarce Effective utilization of resources is required OR models can provide useful support

q/.r NSRZKLA4-P3 Dutch railway quantities passengers per workday passenger kilometers per year 5000timetabled trains per workday 2800 kilometers of tracks 380stations 2650wagons 3000train drivers 4000conductors (and assistants)

q/.r NSRZKLA4-P Ut Hmla WdGd Cps Nwk Rta Rtn Rtd Vtn MdaGdg Hourly Pattern for the track Rotterdam - Utrecht 2800

q/.r NSRZKLA4-P5 Platform Occupation Chart for Utrecht Central

q/.r NSRZKLA4-P6 Utilization of the infrastructure (%) Price per pkm in cents (Dfl) Dispunctuality (%) Source: Koppeling Dec 16, 2000

q/.r NSRZKLA4-P7 Capacity aspects (infrastructure) Passengers vs. Cargo vs. Maintenance Significant increase in demand is expected Stations are a major bottle-neck # Trains or # Passengers/Tons? Utilization vs. Robustness Different kinds of capacity (OptiRail) Theoretical capacity Practical capacity Planned capacity

q/.r NSRZKLA4-P8 Capacity aspects (infrastructure: tracks) # Parallel tracks Heterogeneity of traffic # Take-over facilities Safety system (length of blocks) Energy system (diesel/electric) Rolling stock characteristics Rolling stock capacity (per wagon/unit) Environment (noise)....

q/.r NSRZKLA4-P9 Capacity aspects (infrastructure: stations) # Platforms # Parallel/simultaneous routes Platform occupation times (length of return times) # Shunting movements # (Cross-platform) connections Length of platforms Rail-side vs. City-side....

q/.r NSRZKLA4-P10 Traditional system time A BCDE F 5 trains

q/.r NSRZKLA4-P11 Clustered time 7 trains A BCDE F

q/.r NSRZKLA4-P12 A BCDE F Take-over time 9 trains

q/.r NSRZKLA4-P13 Homogeneous system time A BCDE F 8 trains

q/.r NSRZKLA4-P14 A BCDE F 2 tracks per direction time 15 trains

q/.r NSRZKLA4-P15 Capacity analysis and utilization DONS/SIMONE:Feasibility and robustness (dependent on timetable) Model Huisman: Network of queuing systems (independent of timetable) OptiRail: Network flow model with discrete resources (independent of timetable) B & B:Benutten & Bouwen (Utilize & Expand)

q/.r NSRZKLA4-P16 Rolling stock In rush hours:Allocation of scarce capacity Outside rush hours:Efficiency

q/.r NSRZKLA4-P17 q/.r Mat’64 with 2 or 4 wagons Koploper with 3 or 4 wagons Double decker with 3 or 4 wagons

q/.r NSRZKLA4-P18 Capacity aspects ( Rolling stock) Increasing demand during last years Additional wagons (units) will be available soon Rolling stock capacity mainly determined by - available # of wagons (units) - capacity per wagon (unit) - speed of the trains Available operational rolling stock capacity = (rolling stock capacity) - (maintenance reservation)

q/.r NSRZKLA4-P19 Capacity aspects ( Rolling stock) Required operational capacity mainly determined during the morning rush hours Allocated capacity per trip => minimally required capacity - shortage Allocated capacity per trip = # wagons (units) * capacity per wagon (unit) Maximum train length <= minimum platform length

q/.r NSRZKLA4-P20 Minimally required capacity per trip Based on counts by conductors

q/.r NSRZKLA4-P line 1 line 2 Eight o’clock cross section

q/.r NSRZKLA4-P22 Rolling stock allocation model Applied to 8 o’clock cross section of all stoptrains Implemented in ILOG OPL Studio Solved by CPLEX 7.0 on PC (900 MHz, 256 Mb) # variables: 3700 # constraints:9600 Manual solution: Total shortages (2nd class)4869 # trains with shortages 75 (of 188) Scenarios based on max. # types and subtypes per line: Best solution found:3958 # trains with shortages 71 (of 188)

q/.r NSRZKLA4-P23 01 Utilization Waiting time Waiting time vs. Utilization

q/.r NSRZKLA4-P24 Conclusions Capacity planning at several levels Relevant resources are: ¶ Infrastructure ¶ Rolling stock ¶ Personnel ¶... All relevant resources are scarce Effective utilization of resources is required OR models can provide useful support

q/.r NSRZKLA4-P25 Conference on Optimization in Public Transport May 23, 2002, Erasmus University Rotterdam Airline session: Jacques Desrosiers GERAD and École des Hautes Études Commericales, Montréal Gerrit Timmer; ORTEC Consultants and Free University Amsterdam Railway session: Paolo Toth; DEIS, University of Bologna, Italy Leo Kroon; NS Reizigers and ECOPT, Erasmus University Rotterdam Bus session: Matteo Fischetti; DEI, University of Padua and Double-Click sas, Italy Dennis Huisman; ECOPT, Erasmus University Rotterdam