Train Movements Planning at a Railway Terminal Station

1

Train Movements Planning

at a Railway Terminal Station

Railway Workshop 2019

IEOR, IIT Bombay

Shripad Salsingikar

PhD scholar, IEOR, IIT Bombay

Narayan Rangaraj

Professor, IEOR, IIT Bombay

21 June 2019

2Salsingikar | Railway Workshop 2019 | 21-Jun-2019

Outline

Introduction

Problem definition

Solution approach

Experimental study

Conclusions & Future Work


Definitions

Routing: Finding a path for a set of train services in a railway network

– Global Routing

o Finding a sequence of stations to visit for each train

– Local Routing

o Finding a sequence of track resources (section, loop) to

occupy for each train

Scheduling: Temporal allocation of tracks to a set of train services

– Allocating track resource to trains (Local) Routing

– Determining occupation start time and end time for allocated tracks for each

train


Motivation

Terminal station at a sub-urban network is resource constraint

– Limited platforms, quick turn around, cross movements

– Bottleneck areas in the network

– Passenger flow and convenient

Train movement planning at terminal involves

– Finding traversal paths for trains through the network

– Assigning platforms and tracks to trains

– Planning activities like train reversal, loco reversal

Performance parameters not well defined

– Unlike line section, passenger trains and freight trains


Problem definition

Finding a conflict free path for each train through the terminal

– Assigning track resources to a set of trains and related activities

– Satisfying operational and safety

Operating policies –

– Route Lock Route Release, Route Lock Section Release, Section

Lock Section Release

Output – Train schedule at the junction

Key decisions

– Allocating path and tracks to each train

– Deciding time interval and sequence of trains


Literature Gaps

Gaps:

No explicit modeling of reversal / shunting activities

Comparison of all operating policies is missing

No study involving planning problem occurring in India

Combined simulation and optimization approach is rare

Work:

Simulation approach for junction planning (Junction)

Does not make any decision but execute previously made ones

Useful for capacity analysis

Mathematical optimization approach (Terminal)

Useful for timetabling as well as capacity analysis


Solution Approach


Layout

Inbound Paths A – D – C

Outbound Paths C – D – A


Features

Microscopic details of railway network

Models activities like train reversal, loco reversal

Considers operating policies like route-lock route-release,

route-lock section-release and section lock section-release

Considers train length based clearance time

Pseudo speed dynamics - considers different path run times


Model

Objectives :

– Minimize sum of total time spent by the train in the system,

– Halt time for each train,

– Occupancy time for each track resource,

– Number of track resources used by trains

Variables:

– Path allocated to train

– Sequence in which train would occupy each track

– Occupation start & end time for each track in a path for each train

– Lock start time & end time for each track in a path for each train


Model Cont…

Constraints:

– A train has to be allocated to exactly one inbound path

– A train has to be allocated to exactly one outbound path

– Inbound & outbound path allocated should form a valid route

– Each track in the path should be allocated when a path is chosen

– A train cannot arrive earlier than expected arrival time

– A train must not depart earlier than scheduled departure time

– Two trains following each other on a track element should be

separated by a minimum separation time (headway)


Model Cont…

Constraints:

– departure time >= arrival time + run time + clearance time

– departure time >= arrival time + run time + clearance time + halt time

– arrival time next edge >= arrival time prev edge + run time

– arrival time next edge >= arrival time prev edge + run time + halt time

– departure time prev edge >= arrival time next edge + clearance

– arrival time next edge >= departure time prev edge – clearance

Route-lock route-release policy

– Reserve all block elements simultaneously

– Release all block elements (other than the last element)

simultaneously, when train reaches the last element.


Constraints Depictions

Arr1

Arr2

Dep

1

Dep

2

Arr1

Arr2

Dep

1

Dep

2

Turnaround,Headway,CrossoverConstraints


Different Topologies


Layouts - Terminals


Layouts - Terminals


Layouts - Terminals


Layouts - Station


Layout - Junction


Layout - Junction


Case Study


Case Study

Instance

– A real life terminal station extracted from Indian Railways network.

– The traffic and complexity of this instance is artificial and only for

illustration but is closer to reality

– Due to typical topology layout not possible to have a fixed

headway between two consecutive trains

Demonstrate

– How mathematical model can be used for coming up with new

timetable

– Explores how this approach can be used for analyzing the impact

of headway, halt time on delay and utilization


CSMT Network- Scissor


CSMT Network- Concave


CSMT Network- Convex


Instance & Computations

A set of 25 homogenous trains arriving at the system boundary

with fixed inter arrival time (called ‘Headway’)

InterArrTime is varied between 0 to 300 with step size of 30 [21]

Halt of train is varied between 60 to 300 with step size of 60 [5]

Three network topologies – {Scissor, Concave, Convex} [3]

Train length – 250 Meters, Entry speed – 50 km/h

Acceleration – 0.8 m/s2, Deceleration – 1 m/s2

Speed limit – Crossing edges = 15 km/h, Other edges = 50 km/h


Data Setup

Timetable is computed for 315 scenarios (21*5*3)

– Solver - ILOG CPLEX and C++

– Timeout - 3600 sec

– Machine - Ubuntu 3.6 GHz 4 GB RAM

Various parameters like ideal operating headway, delay, track

utilization is analyzed and presented

Outputs

– Congestion Train waiting time at entry

– Overall make-span Exit time of last train – Entry time of first train

– Train make-span Exit time of train – Entry time of train

– Allocation & utilization Platform edge and all edges


Halt time – 180; Network – Scissor

Platform Allocation Headway and Wait Time

Track Utilization Run Time and MIP Gap


Halt time – 180; Network – Concave




Halt time – 180; Network – Convex




Halt time – 180; Network – All

System Utilization @ headway = 0 Planned headway between two trains


Headway = 0 ; Network – All


Observations

Ideal headway to operate in all layout is 240 sec.

Trains took shortest route i.e. Route1 most of the time

# of trains allocated to each platform fluctuates, possibly due to multiple

optima

Time spent in the system by train is same at all headway

No acquired delay in the system, only network entry delay (waiting)

For sub-optimal instances MIP gap is less than 14%

Convex layout is best among three layout studied

Convex layout has lowest track occupation for headway <= 420 sec

Owing to network topology the headway between two trains is not same

Convex layout has best ideal headway for all halt times


Conclusions

Presented a mathematical optimization approach for train

timetabling at junction

Explicit modelling of activities like train reversal, loco

reversal

Explicit modelling of operating policies

Proposed methodology can be used for

– Developing an operational plan for a junction

– Determine the capacity of the junction

– Assessing the impact of halt time and inter arrival time on

the acquired delay and resource utilization under different

scenarios


Publications

Salsingikar, S., Albert, S. Rangaraj, N., and Awad, A. (2019), 'Analysis and planning of train

movements at a terminal station'. {draft ready}

Salsingikar, S. and Rangaraj N., (2016), "Freight train routing and scheduling in a large railway

network", Presented in OR-2016, Hamburg, Germany, 30 Aug - 02 Sep 2016.

Salsingikar, S., Sathishkumar L., Rangaraj, N. and Awad, A. (2017). "Analysis and planning of train

movements at a complex railway junction", Presented in RailLille2017, Lille, France, 4-7 Apr 2017

Raut S., Sinha S. K., Khadilkar H. and Salsingikar S. (2018), "A rolling horizon optimisation model for

consolidated hump yard operational planning", Journal of Rail Transport Planning and Management,

Article in Press, Oct 2018

Khadilkar H., Salsingikar, S. and Sinha S.K (2017). "A machine learning approach for scheduling

railway networks", Accepted for RailLille2017, Lille, France, 4-7 Apr 2017.

Sinha, S. K., Salsingikar, S., and SenGupta, S. (2016). "An iterative bi-level hierarchical approach for

train scheduling", Journal of Rail Transport Planning & Management. vol. 6(3), pp 183-199.

Sinha, S. K., Salsingikar, S., and SenGupta, S. (2015). "Train scheduling using an iterative bi-level

hierarchical approach", Presented in RailTokyo2015, Tokyo, Japan, 23-26 Mar 2015.


References

Awad, A. and Rangaraj, N. (2015). Hybrid simulation of railway traffic in a complex dispatching area.

In 27th European Conference on Operational Research (EURO2015), Glasgow, UK.

Corman, F., Goverde, R. M., and D’Ariano, A. (2009). Rescheduling dense train traffic over complex

station interlocking areas. In Robust and Online Large-Scale Optimization, pages 369–386. Springer.

Cui, Y. (2010). Simulation based hybrid model for a partially automatic dispatching of railway

operation. Phd Thesis, University of Stuttgart.

Dorfman, M. and Medanic, J. (2004). Scheduling trains on a railway network using a discrete event

model of railway traffic. Transportation Research Part B: Methodological, 38(1):81–98.

Dewilde, T., Sels, P., Cattrysse, D., and Vansteenwegen, P. (2013). Robust railway station planning:

An interaction between routing, timetabling and platforming. Journal of Rail Transport Planning &

Management, 3(3):68–77.

Espinosa-Aranda, J. L. and García-Ródenas, R. (2012). A discrete event-based simulation model for

real-time traffic management in railways. Journal of Intelligent Transportation Systems, 16:94–107.

Lusby, R. M., Larsen, J., Ehrgott, M., and Ryan, D. (2011). Railway track allocation: models and

methods. OR spectrum, 33(4):843–883.

Lusby, R. M., Larsen, J., Ehrgott, M., and Ryan, D. M. (2013). A set packing inspired method for real-

time junction train routing. Computers & Operations Research, 40(3):713–724.

Pellegrini, P., Marlière, G., and Rodriguez, J. (2014). Optimal train routing and scheduling for

managing traffic perturbations in complex junctions. Transportation Research Part B:

Methodological, 59:58–80.

37

Thank You!

38

Mathematical Model


Mathematical Model

Variables:

𝐸 Set of track elements, indexed by 𝑒

𝑃 Set of paths. indexed by 𝑝 (ordered sequence of connected tracks)

𝑅 Set of routes indexed by 𝑟 (ordered sequence of connected paths)

𝑇 Set of trains, indexed by 𝑡

𝑃𝐼 ⊂ 𝑃 Set of Inbound paths (Paths bet Home signal and Halt signals)

𝑃𝑂 ⊂ 𝑃 Set of Outbound paths (Paths bet Halt signals and Out signal)

𝐸𝑝 Set of track elements that belongs to path 𝑝

𝐴𝑇𝑡,𝐷𝑇𝑡,𝐻𝑇𝑡 Expected arrival time, departure time and halt time for train 𝑡

𝑁𝑆𝑠,𝑋𝑆𝑡, HS Entry Signal and Exit signal train 𝑡. Set of halt signals.

𝑃𝑡, 𝑃𝐼𝑡 , 𝑃𝑂𝑡 Set of paths, inbound and outbound train 𝑡 can access


Mathematical Model

Variables:

𝑦𝑡,𝑝 Variable indicating if train 𝑡 is allocated to path 𝑝

𝑥𝑡,𝑒 Variable indicating if train 𝑡 is allocated to track 𝑒

𝐹𝑡,𝑡′,𝑒 Variable indicating if train 𝑡 occupy arc 𝑒 after train 𝑡′ where 𝑡 ≠ 𝑡′

𝑎𝑡,𝑒 Arr. time for train 𝑡 at track 𝑒, when head of train 𝑡 start occupying 𝑒

𝑑𝑡,𝑒 Dep time for train 𝑡 at track 𝑒, when tail of train 𝑡 leaves 𝑒

𝑢𝑡,𝑒 Lock start time for train 𝑡 at track 𝑒

𝑣𝑡,𝑒 Lock end time for train 𝑡 at track 𝑒


Mathematical Model

Objectives:

Minimize total time spent by the train in the system.

min 𝑡 ∈ 𝑇𝑒 = 𝑖,𝑗 ∶𝑗=𝑋𝑆𝑡

(𝑑𝑡,𝑒 − 𝐴𝑇𝑡) + 𝑡 ∈ 𝑇𝑒 ∈ 𝐸

{ 𝑑𝑡,𝑒 − 𝑎𝑡,𝑒 + 𝑣𝑡,𝑒 − 𝑢𝑡,𝑒 + 𝑥𝑡,𝑒 }

Constraints:

A train has to be allocated exactly one inbound path and one outbound path

𝑝 ∈ 𝑃𝐼𝑡(𝑦𝑡,𝑝) = 1 ∀ 𝑡 ∈ 𝑇 (1)

𝑝′ ∈ 𝑃𝑂𝑡(𝑦𝑡,𝑝′) = 1 ∀ 𝑡 ∈ 𝑇 (2)

𝑝′∈ 𝑃𝑂𝑡 : (𝑝,𝑝′)∈𝑅𝑡 𝑦𝑡,𝑝′ ≥ 𝑦𝑡,𝑝 ∀ 𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃𝐼𝑡 (3)

Each element in the path should be allocated when a path is chosen

𝑥𝑡,𝑒 ≥ 𝑦𝑡,𝑝 ∀ 𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃𝑡 , 𝑒 ∈ 𝐸𝑝 (4)


Mathematical Model


Mathematical Model


Mathematical Model

Route lock – route release policy

𝑢𝑡,𝑒′ ≤ 𝑎𝑡,𝑒 −𝑀(1 − 𝑦𝑡,𝑝) ∀ 𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃𝐼𝑡 , 𝑒′ ∈ 𝐸𝑝, 𝑒 ∈ 𝐸𝑝 ∶ {𝑒 = 𝑖, 𝑘 ∶ 𝑖 = 𝑁𝑆𝑡} (R1a)

𝑢𝑡,𝑒′ ≤ 𝑎𝑡,𝑒 −𝑀(1 − 𝑦𝑡,𝑝) ∀ 𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃𝑂𝑡 , 𝑒′ ∈ 𝐸𝑝, 𝑒 ∈ 𝐸𝑝 ∶ {𝑒 = 𝑖, 𝑘 ∶ 𝑖 ∈ 𝐻𝑆} (R1b)

𝑣𝑡,𝑒′ ≥ 𝑑𝑡,𝑒 −𝑀(1 − 𝑦𝑡,𝑝) ∀ 𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃𝐼𝑡 , 𝑒′ ∈ 𝐸𝑝, 𝑒 ∈ 𝐸𝑝 ∶ {𝑒 = 𝑖, 𝑘 ∶ 𝑘 = 𝐻𝑆} (R1d)

𝑣𝑡,𝑒′ ≥ 𝑑𝑡,𝑒 −𝑀(1 − 𝑦𝑡,𝑝) ∀ 𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃𝑂𝑡 , 𝑒′ ∈ 𝐸𝑝, 𝑒 ∈ 𝐸𝑝 ∶ {𝑒 = 𝑖, 𝑘 ∶ 𝑘 = 𝑋𝑆𝑡} (R1e)

Route lock – section release policy

01-15, R1a and R1b

𝑣𝑡,𝑒 ≥ 𝑑𝑡,𝑒 −𝑀(1 − 𝑥𝑡,𝑒) ∀ 𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃𝑡 , 𝑒 ∈ 𝐸𝑝 (R2)

Section lock – section release policy

01-15, R1c, R1d & R1e and below constraints

𝑎𝑡,𝑒 ≤ 𝑢𝑡,𝑒 −𝑀(1 − 𝑥𝑡,𝑒) ∀ 𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃𝑡 , 𝑒 ∈ 𝐸𝑝 (R3)


Minimize total time spent by the train in the system.

46

References


Literature Review

General Review

– Lusby et al 2011, Fang et al 2015, Cui 2010

Exact approach– Platform allocation (Lusby et al 2011)

– Caimi et al 2011 – Limited routes, not fixed, fixed speed, resource tree conflict

graph, heuristics, time discretization, track circuit no route definition.

– Corman et al 2009 – Route are fixed, post processing for variable speed.

Compares RLRL (Meso) and RLSR (Micro). Alternative Graph.

– Pellegrini et al 2014 – Routes are not fixed, speed is fixed. Compares RLRL and

RLSR. MILP on microscopic n/w, rolling horizon

Simulation approaches– Simulation based approach for single line (Dorfman & Medanic 2004, Li et al 2008)

as well as sub-urban railway (Espinosa-Aranda 2012)

– Agent-based discrete-event simulation for modeling complex dispatching, section-

lock section-release policy (Awad & Rangaraj 2015)

– RailSys, OpenTrack - long-distance and middle-distance distance railways


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Documents

Train Movements Planning at a Railway Terminal Station