C. Tyler Dick, P.E.
University of Illinois at Urbana-Champaign
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• Introduction
• Basic Rail Capacity Concepts
• Analytical Models of Railway Capacity
• Parametric Models
• Simulation Models
• Optimization Models
• Other Considerations and Expansion Strategies
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• Analytics
• Data mining
• Network optimization
• Queuing theory
• Regression modeling
• Risk modeling
• Simulation
• Utility models
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• 19 th and early 20 th century: Great expansion of railroads
• World War I: War traffic brought network to standstill due to insufficient capacity due to inefficient operations
• 1920s: Relative balance between capacity and traffic levels
• Great Depression: Loss of traffic led to excess capacity
• World War II: Congestion from war traffic
• After WWII: Overcapacity as passenger and freight traffic declined
• 1990 - Current: Growth in traffic and market power has permitted railroads to spend substantial amounts to remove choke points
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Freight Growth
Low Cost
Transportation
Reliability Intercity Passenger Trains
Commuter Service
Environment
Cambridge Systematics. (2007). National Rail Freight Infrastructure Capacity and Investment Study.
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• Inability to handle more traffic
• Decreasing level of service
• Diminished ability to recover from a disruption
• Limited windows for track maintenance
• Increase time in yards, terminals and stations
• Increase cycle times
• Increase number of trainsets, rolling stock
• Increase number of crews (hours of service limitations)
• All of the above increase costs
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• Railway infrastructure is capital intensive and a long-term investment
• Capacity lags behind changing demands
Capital Investment as a % of Revenue
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• Transportation Network
• Railroad Network
• Subdivision or Line
• Yards & Terminals
• Stations & Platforms
• Interlockings & Junctions
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• Practical Capacity: Ability to move traffic at an
“acceptable” level of service
• Economic Capacity: The level of traffic at which the costs of additional traffic outweighs the benefits
• Engineering Capacity: The maximum amount moved before the system ceases to function
• Ultimate Capacity: Breakdown conditions at maximum train density. The system has ceased to function and all signals are red
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Amount Moved
Trains
Railcars
Gross Tons
Revenue Tons
Passengers
TEUs
(Per Year)
(Per Day)
(Per Hour)
(Per Peak Hour)
Reliability
Distribution of Arrival Times
Average Delay
Standard Deviation of Delay
On Time Performance
Right Car Right Train
Crew Expirations
Velocity
Utilization
Terminal Dwell
Blocking Time
Signal Wake
Train Miles/Track Mile
Cycle Time
Trainsets or Railcars On-Line
Track Occupation
Train Density
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Unlike highways, there is no standard railroad capacity model
• The complex nature of railroad operations and limited research funding has prevented a universal capacity model from being developed
• Currently several different models are in use
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• Higher delays correspond to a lower level of service (LOS)
• Maximum theoretical train volumes are never reached due to deteriorated level of service
• Acceptable level of service establishes maximum train volume
Abril, M., Barber, F., Ingolotti, L., & Salido, M. (2008). An assessment of railway capacity. Transportation Research Part E: Logistics and
Transportation Review , 44 (5), 774-806.
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Different Traffic and Track Configurations will Change Delay-Volume Relationship
Acceptable Delay
Volume (Trains/D ay)
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• Number of tracks
• Siding length
• Siding spacing
(distance & time)
• Crossover spacing
• Single crossovers
• Universal crossovers
• Parallel crossovers
• Geometry
• Grade
• Curvature
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• Common on most transit and some commuter rail operations
• Each track has a dedicated “current of traffic” with trains separated by a minimum headway
• Headway is a function of safe braking distance and signal spacing or control block length
• Very high capacity if all trains in one direction travel at the same speed (i.e. no passing)
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• Single direction on double track
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Double-Track Analytical Model:
Maximum Throughput Calculation
• The maximum traffic flow that a rail line can accommodate under ideal condition
Where:
N = Number of trains per day
1440 = Number of minutes in a day
H min
= Minimum headway (minutes)
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• Passenger trains travel at higher speeds than freight trains
• Speed differential leads to decreased capacity
• Passenger train on freight corridor
• Freight train on passenger/commuter corridor
Time
• 1 minority train consumes 3 majority train slots
Time
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• Passenger or commuter trains may experience additional delay while trailing behind slower trains
• If control system allows, faster trains can use opposite track to overtake slower trains
• Interrupts flow of traffic in opposite direction, decreasing overall capacity
• A passenger train requires over 40 miles to pass a freight at track speed without delay to either train
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Single-Track Operation: Meet and Pass
• Single track poses significantly more challenges for practical railway capacity
• No longer simply limited by train spacing
• Must consider “meets” of trains traveling in opposite direction
• These impose constraints on schedule
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Single-Track Analytical Model:
Return Grid Calculation for Meets
• Capacity of single track with meets
C = Capacity in trains per day
1440 = Number of minutes per 24 hours t = Minutes to travel between sidings t/2 = Average dwell time waiting for opposing train to arrive m = Delay for each meet due to braking, entering the siding, running the length of the siding, leaving the siding and accelerating to speed
2 = number of trains per pair
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Siding A
Time 0
Time t
Time t+m
Time t+m+t/2
Time 2t+m+t/2
Siding B
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• Differing train operating speeds causes deviations from regular return-grid model, decreasing capacity
Time
Time
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T
2
Pass Delay
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Heterogeneous Operations and Capacity
• Simple headway and grid models only work when all trains operate at the same speed
• Actual trains have different
• Operating speed
• Acceleration and braking characteristics
• Priority
• Station stopping patterns
• Particularly apparent where passenger and freight operations share track infrastructure
• From a capacity perspective:
1 freight train ≠ 1 passenger train
• These differences decrease capacity and require more complicated capacity analysis tools
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• Parametric Models are developed from statistical analysis of collected operating or simulation data
• Key infrastructure and operating parameters are identified to predict a delay-volume curve
• Attributes include
• Average speed
• Speed ratio
• Priority
• Peaking
• Siding spacing and uniformity
• Percent double track
• Signal spacing
• FRA and CN have well-known parametric models
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Average Speed
Speed Ratio
Priority
Peaking
Siding Spacing
Siding Spacing Uniformity
Signal Spacing
Track Outage
Slow Orders
% Dbl Track
Maintenance
44.38
1.113
0.342
1.727
7.77
0.49
0.93
0
0
75
0
Average Speed
Priority
Siding Spacing
Signal Spacing
44.4 mph Speed Ratio
0.342
Peaking
7.77 miles Uniformity
0.93
% Double Track
70
1.113
1.727
0.49
50
60
50
40
30
20
10
0
0 10 20 30
Volume (Trains per Day)
40
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Conference . Phoenix, 1999. 1194-1200. Web. 21 May 2012.
50 60
31

• Calculate train movements and make decisions under the same rules as railroad dispatchers
• Account for different equipment types, train consists, train handling characteristics, terrain and track conditions
• Common uses of Simulation Tools:
• Develop operating plans
• Diagnose bottlenecks and recommend schedule changes
• Evaluate various capital improvement scenarios
• Assess the impact of adding new trains to a network
• Many simulation models are available depending on the purpose and task of the study
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• Passenger timetable development (passenger)
• OpenTrack
• Viriato
• Specify timetable and identify conflicts
• RailSYS
• RailEval
• Non-timetable (freight) and resolve conflicts with dispatching logic
• Rail Traffic Controller
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• Identify required system settings to achieve an optimal level of performance
• Can become computationally complex for large railway networks with multiple train types
• Example applications
• Passenger timetable development
• Station platform and track assignment
• Rolling stock and crew cycles
• Infrastructure investments for running time improvement on shared corridors
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• Operations options:
• Increase average speed
• Reduce traffic peaking
• Reduce the variability in speed
• Reduce number of meets & passes
• Increase length & weight of trains
• Improved acceleration and braking
• Scheduling
• Infrastructure options:
• Add or lengthen passing sidings
• Additional tracks
• Add staging and terminal tracks
• Add station platforms
• Improve junction design
• Grade separations
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• Fleeting
• Train Type: Reduce delays due to different train types operating on the same line
• Train Direction: Reduce delays on single tracks lines by reducing the meet delay
• Express and Skip-Stop scheduling
• Decrease travel time by bypassing intermediate station and terminals
• Minimize conflicts with trains in the same direction
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Incremental Capacity of
Infrastructure Expansion
ST, siding every 21.4 miles bidirectional running, DT directional running, DT
Volume (trains/day)
Kahn, Ata M. Railway Capacity Analysis and Related
Methodology . Ottawa, 1979. Print.
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• New passing siding
• $8 million and up
• Second main track
• $1 million per mile for rail, ties and ballast
• $4-6 million per mile depending on embankment, drainage and signals
• Bridges, grade separations and tunnels can quickly increase costs
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• Mainline capacity consumed by
• Local service to freight rail customers
• Deadhead and repositioning moves
• Passenger boarding delays
• Locomotive and rolling stock failures
• Track inspection
• Track maintenance
• Difference between practical and engineering capacity
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• Models that capture yard-mainline interaction
• Predicting the impact of higher speed passenger and freight trains on the same corridor
• Creating new theoretical & parametric models
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Copyright Restrictions and Disclaimer
Presentation Author
C. Tyler Dick, P.E.
Senior Railway research Engineer
Department of Civil and Environmental Engineering
University of Illinois at Urbana-Champaign
205 North Mathews Ave
Urbana IL 61801
217-300-2166 ctdick@illinois.edu
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