Ways of Deriving Train Delay Relationships

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Ways of Deriving Train Delay Relationships

• Lars-Göran Mattsson
• Department of Transport and Economics
• Royal Institute of Technology
• Stockholm

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Introduction

• Reliability of train services is an important
  performance indicator
• Relevant for investment planning, timetabling and
  operational planning
• We need validated relationships between the
  design and utilisation of the system and the
  amount of delays
• A review of ways of deriving such relationships
• Analytical approaches
• Micro-simulation approaches
• Statistical approaches

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What is special with railway service?

• Safety in focus
• Disturbances and fault are not allowed to reduce
  safety rather delays
• Impossible to pass an obstacle on the track
• Many subsystems in series (track, signal, power
  systems, rolling stock, crews etc.)
• Controlled and regulated system
• These properties make the railway system
  sensitive to disturbances

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Terminology

• Delay actual running time minimum running time
• Scheduled delay scheduled running time
  minimum running time
• Unscheduled delay actual running time
  scheduled running time
• Unscheduled delay primary delay secondary
  delay
• Primary delay delay caused by some external
  exogenous circumstance
• Secondary delay delays that are caused by other
  trains and hence are increasing with capacity
  utilisation

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Capacity

• Capacity ? maximum number of trains that can
  operate on a railway section during a given time
  period (maximum train flow fmax)
• Capacity is determined by the maximum of the
  product of speed v and density d according to the
  general law of traffic fmax max(v ? d)
• dmax depends e.g. on the number of tracks (single
  track ? meetings double track ? overtakings)
  and on the timetable (speed heterogeneity)
• Capacity consumption the time the rail section
  is occupied as a percentage of the considered
  time window

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Large economies of scale in capacity provision
? Two stations 50 km apart ? 5 min buffer time
for meeting ? 5 min minimum headway ? 5 min for
overtaking
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Analytical delay analysis

• Huisman och Boucherie (2001)
• Trains in one direction without overtaking
  possibilities
• Single section no network analysis
• Delays caused by slower trains obstructing
• faster trains
• Relies on queuing theory
• Both for strategic and operational planning
• Moderate data demanding

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Regional (R), inter-regional (IR) and inter-city
(IC) trains with minimum running time of 48, 36,
33 min for a 67 km section. Random order,
exponential headway, however minimum 2 min. The
same intensity for all train types Source
Huisman and Boucherie (2001)
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Micro-simulation approaches

• Detailed delay analysis requires micro-simulation
  
• RailSys is a system for timetable design that has
  been applied in Sweden
• Can also be used for delay analysis
• Requires detailed data about tracks, signals,
  block sections, gradients, train types
  (acceleration, deceleration), timetable
• Possible to simulate random arrival pattern of
  the trains, stochastic dwelling times at the
  stations
• Resource demanding analysis

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Simulation of a major technical breakdown

• Fire in the interlocking system at a station
• All signals at the station were put out and the
  switches could not be used
• Reopened as a double-track instead of four tracks
  and with a manual signal system
• Maximum speed reduced to 40 km/h
• Only half of the traffic was allowed (66 trains
  per day)
• After extensive calibration ? simulated mean
  delay 16.1 min versus 17.6 min in reality

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Mean delay (hhmm) by time of the day
More trains 84, the same 66, fewer 50 per
day
Source Wiklund (2003)
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Mean delay per day (hhmm) /- one standard
deviation
Train/h
Source Wiklund (2003)
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Consumers perspective on reliability

• So far producers perspective
• Delayed trains
• Consumers perspective more interesting
• What is the travel time uncertainty for a journey
  from A to B?
• Not only delayed trains/buses
• Missed connections important
• Rietveld et al. (2001) have developed a
  methodology
• Random sample of journeys
• Running time statistics for sections of the
  journeys
• Independence assumption
• Possible to simulate the travel time uncertainty
  for the whole journey

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Mean simulated travel time as a percentage of
scheduled travel timeA sample of Dutch journeys
Source Rietveld et al. (2001)
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Statistical approaches

• Real data
• Regression analysis of the relationship between
  capacity consumption and secondary delay
• Gibson et al. (2002) report on one such study
  from Britain
• Dit Aiexp(?Cit) with 1 lt ? lt 4
• Could also be interesting to relate delays to
  extreme weather conditions
• Simulated data
• Could be an interesting possibility

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Conclusions 1

• Surprisingly little published on cause-effect
  relationships for train delays
• Most studies has a supply or producer perspective
• A demand or consumer perspective would be more
  interesting
• More or less impossible to model the causes of
  primary delays
• Should be possible to find relationships between
  the amount of primary delays and technical
  standard, maintenance activities, weather
  conditions etc.

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Conclusions 2

• How primary delays and capacity consumption
  affect secondary delays could be studied by
• analytical approaches
• micro-simulations approaches
• statistical approaches
• Analytical approaches
• Requires not so much data
• Limited computational burden
• Leads to less detailed results
• Particularly useful for strategic decisions

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Conclusions 3

• Micro-simulations approaches
• Requires detailed data (infrastructure, trains,
  timetable)
• Enables detailed analyses
• Particularly useful for construction of robust
  timetables
• Statistical analysis of simulated delays
• Could be carried out as a statistical experiment
• Requires an extensive series of simulations
• Is probably the most reliable way of deriving
  cause-effect relationships for train service
  reliability