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Analysis of the impact of speed variation dynamics on the optimization ofthe real-time railway traffic management problem
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University of TriesteDepartment of Engineering and Architecture
Master Degree in Computer Engineering Master student: Martino Marangon
Supevisor: Lorenzo Castelli Co-supervisor: Paola Pellegrini
Introduction
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Introduction
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Railway Infrastructure● Track circuit: portion of track where the presence of a train is
detected automatically● Block section: it is composed by one or more track circuit
○ Delimited by two main signals○ Different block sections may share one or more track circuits
● Route: ordered sequence of block sections, that links an origin-destination pair
Introduction
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Block section● When a train enters the first track circuit of a block section, all the
following are reserved to it● If a train uses a track circuit, no other train can use it.● Utilization: both physical occupation and prior reservation● For safety reason, only one train can use the same block section at
the same time.● The aspects of a signal indicate to a train driver the behaviour that
has to be followed○ Green aspect: two following block sections are free ⇨ train can
proceed at designed speed○ Yellow aspect: following block section is free, following one is used by
another train ⇨ the train has to decelerate and reach a complete stop before the next signal
○ Red aspect: following block section is used by another train ⇨ train must reach a complete stop before the signal
Martino Marangon
Real-time railway traffic management problem
(rtRTMP)
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Real-time railway traffic management
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Train Delay● Primary Delay: when a train suffers of a certain amount of
delay due to unexpected events (technical failure)● Secondary Delay: when a train suffers of a certain amount of
delay caused by the delay of another train
Due to the interaction between trains, these delays may propagate along the whole network generating knock-on delay
rtRTMP● Consists in selecting the train routes and schedules in order to
minimize the propagation of delays● Time constraints: time interval to compute a solution is strictly
limited
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Modeling rtRTMPThe modelling approaches to rtRTMP can be divided into two classes:
● Fixed-speed models: speed profile of a train is not updated in case of conflict
Real-time railway traffic management
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● Variable-speed models: the speed profile of a train is modelled in order to include possible consequences of conflicts
Real-time railway traffic management
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Modeling rtRTMP● Variable-speed model: complete and accurate but difficult to
solve in short computation time● Fixed-speed model: require less computation time● The fixed-speed model is the most used
Objective● Develop a variable-speed program that can be used to
evaluate the conflict solution computed by fixed-speed algorithms○ RECIFE-MILP algorithm
Real-time railway traffic management
Objectives of the study:
1. Develop a program to model Infrastructure and Rolling Stock
2. Develop a program to compute running times in absence of traffic
3. Develop a program that can be used to evaluate the solutions of the RECIFE-MILP algorithm
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Objectives of the study:
1. Develop a program to model Infrastructure and Rolling Stock
2. Develop a program to compute running times in absence of traffic
3. Develop a program that can be used to evaluate the solutions of the RECIFE-MILP algorithm
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Modelling Infrastructure and Rolling Stock
Context:● RECIFE Project
○ Rodriguez et al., RECIFE: Models and Tools for Analysing Rail Capacity, 2007
Scenarios:● Information in various data structures in several files● Standard format for data representation
○ Infrastructure, Rolling Stock, Timetable, Maintenance work
○ XML files and schemas○ RECIFE Data Structure (RDS)
Proposal:● Develop a program to generate Infrastructure.XML and
RollingStock.XML according to schema defined by RECIFE Data Structure
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Modelling Infrastructure and Rolling Stock
RDS - Infrastructure
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Modelling Infrastructure and Rolling Stock
RDS - Rolling Stock
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Modelling Infrastructure and Rolling Stock
Program to generate Infrastructure.XML and RollingStock.XML
Input:● Various XML and text files containing several informations
about the Infrastructure and the Rolling Stock○ OpenTrack output○ Handmade Files
Output:● Infrastructure.XML● RollingStock.XML
These files are used as:● Basis for the development of Running Time Computation
Program● Basis for the development of other programs concerning
railway management in real-time15
Modelling Infrastructure and Rolling Stock
Pierrefitte-Gonesse● Length of the line ~ 16 km● Running Time ~ 7 minutes and 40 seconds● 79 Block Sections and 89 Track Circuits
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Modelling Infrastructure and Rolling Stock
Rosny sur Seine - St. Etienne du Rouvray● Length of the line ~ 70 km● Running Time: ~ 23 minutes and 27 seconds high speed trains,
26 minutes and 57 seconds passenger trains, 41 minutes and 3 seconds freight trains
● 10 stations● Presence of gradient
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Objectives of the study:
1. Develop a program to model Infrastructure and Rolling Stock
2. Develop a program to compute running times in absence of traffic
3. Develop a program that can be used to evaluate the solutions of the RECIFE-MILP algorithm
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Running Time Computation
Running Time
● Amount of time that a train needs for travelling along a track circuit
● Duration calculated in absence of traffic● Depends on:
○ Infrastructure characteristics ○ Rolling Stock characteristics
● In order to compute running time:○ Route partitioned into sections of equal characteristics○ Compute Traction Resistance○ Establish if train is in:
■ Braking Section■ Acceleration Section■ Constant Speed Section
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Running Time Computation
Traction Resistance RF:
○ Rolling Stock Resistance RL○ Distance Resistance RD○
Rolling Stock Resistance● Davis mass-independent formula
○ A and B accounts for mass and mechanical resistance○ C refers to air resistance
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Running Time Computation
Distance Resistance RD○ Gradient Resistance RS○ Curve Resistance RB○
Gradient Resistance●● Since railway gradient is very slight
I: inclination [‰]
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Running Time Computation
Curve Resistance
● Roeckl’s formula
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Running Time Computation
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Braking Section
● Maximum speed of the following section is lower than speed of the current section
● Speed reduction must be completed before the following section
Compute Braking Section2 steps:
1. Calculate braking distance to reduce speed from maximum speed vmax1 of current section to maximum speed vmax2 of following section
If sred is shorter than length of current section:i. First part constant speedii. Second part braking section
Running Time Computation
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2. If sred is longer than the length ssec of current sectiona. Compute new maximum speed value for current sectionb.
If the maximum speed of the previous section is greater than the maximum speed of the current section, the braking distance has to be computed for the previous section. For this reason the braking distance is computed in reversed order.
Running Time Computation
Acceleration Section● Maximum speed of the following section is greater than the
maximum speed of current section● 3 possibilities
○ Maximum speed of the section is reached
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Running Time Computation
○ Exit speed lower thanmaximum speed
○ Intersection withbraking curve
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Running Time Computation
Compute acceleration value
● FZ = Z(v) - RF(v,s) traction power surplus○ Z(v) tractive effort○ RF(v,s) traction resistance
● ρ mass factor for rotating masses
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Running Time Computation
Constant speed section
● Train has reached its maximum speed or the maximum speed of a section
● Describe movement: s = v•t● Gradient and curve section:
○ Traction resistance increases, possibly surmounting tractive effort: train decelerates
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Running Time Computation
Running Time Computation Program
● Input:○ Infrastructure.XML○ RollingStock.XML
● Output:○ RunningTimes.txt: running time for each train○ TrainDetails.txt:
■ One for each train■ Detailed information about the train run
○ Gantt.XML
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Running Time Computation
Comparison with OpenTrack● 2 different time steps
○ 1 second: simulation faster but less precise○ 0.1 second: simulation slower but more precise
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Objectives of the study:
1. Develop a program to model Infrastructure and Rolling Stock
2. Develop a program to compute running times in absence of traffic
3. Develop a program that can be used to evaluate the solutions of the RECIFE-MILP algorithm
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Running Time Computation with Traffic
Context● RECIFE-MILP algorithm
○ Pellegrini et al., RECIFE-MILP: An Effective MILP-Based Heuristic for the Real-Time Railway Traffic Management Problem, 2015
○ Tackles the real-time traffic management problem based on the fixed-speed model
Proposal● Given a perturbed situation, use RECIFE-MILP to compute a
set of solutions● Develop a program that can be used to assess the gap
between RECIFE-MILP solutions and solutions computed taking into account the consequences of braking and acceleration phases
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Running Time Computation with Traffic
Running Time Computation with Traffic Program
● Input:○ Infrastructure.XML and RollingStock.XML○ TimeTable.XML○ Disruption.XML: amount of delay that the trains suffer when
entering the infrastructure ○ RECIFESolution.XML: information on train routing and priorities
chosen by RECIFE-MILP algorithm● Output:
○ RunningTimes.txt: infrastructure entrance time, infrastructure exit time and running time for each train
○ TrainDetails.txt:■ One for each train■ Detailed information about the train run
○ SolvedGantt.XML33
Conclusions and Future Work
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Conclusions and Future Work
Running Time Computation Program● For both infrastructures modelled we reached very good results:
the average time difference is around/lower than 1 second for the whole trains’ routes
● Program is very flexible: can be easily modified in order to include:○ Human behaviour of train drivers○ Weather conditions○ Track conditions
Running Time Computation Program with Traffic● For all experiment, the program finds conflict-free solutions
○ Some scenarios different solutions than OpenTrack● Evaluate conflict solutions computed by RECIFE-MILP● Evaluate conflict solutions computed by others algorithms
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Thank you
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