meeting functional requirements for real-time railway

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Ambra Toletti – Marco Laumanns – Peter Grossenbacher – Ulrich Weidmann Conference on Advanced Systems in Public Transport CASPT 2015

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Meeting functional requirements for real-time railway traffic management with mathematical models

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Cordeau JF, Toth P, Vigo D (1998) A survey of optimization models for train routing and scheduling. Transportation Science 32(4):380–404

Törnquist J (2006) Computer-based decision support for railway traffic scheduling and dispatching: A review of models and algorithms. In: Kroon LG, Möhring RH (eds) 5th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS’05), Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, OpenAccess Series in Informatics (OASIcs), vol 2, DOI 10.4230/OASIcs.ATMOS.2005.659

Lusby RM, Larsen J, Ehrgott M, Ryan D (2011) Railway track allocation: models and methods. OR Spectrum 33(4):843–883, DOI 10.1007/s00291-009-0189-0

Corman F, Meng L (2013) A review of online dynamic models and algorithms for railway traffic control. In: Intelligent Rail Transportation (ICIRT), 2013 IEEE International Conference on, pp 128–133, DOI 10.1109/ICIRT.2013.6696281

Cacchiani V, Huisman D, Kidd M, Kroon L, Toth P, Veelenturf L, Wagenaar J (2014) An overview of recovery models and algorithms for real-time railway rescheduling. Transportation Research Part B: Methodological 63(0):15 – 37, DOI 10.1016/j.trb.2014.01.009

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Literature reviews

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Modelling needs assumptions… A farmer has some chickens who don't lay

any eggs. The farmer calls a physicist to help. The physicist does some calculation and says "I have a solution but it only works for spherical chickens in a vacuum!".

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Introduction and motivation Functional requirements Mathematical models Meeting functional requirements with mathematical

models Conclusion and outlook

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Contents

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

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Example: Railway network of the Railway operations laboratory (EBL) at the ETH Zurich

Source: archive of the institute for transport planning and systems (IVT)

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Example: Railway network of the Railway operations laboratory (EBL) at the ETH Zurich

Source: archive of the institute for transport planning and systems (IVT)

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Example: Railway network of the Railway operations laboratory (EBL) at the ETH Zurich

Source: archive of the institute for transport planning and systems (IVT)

Macroscopic representation of the entire network

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Example: Railway network of the Railway operations laboratory (EBL) at the ETH Zurich

Source: archive of the institute for transport planning and systems (IVT)

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Example: Railway network of the Railway operations laboratory (EBL) at the ETH Zurich

Source: archive of the institute for transport planning and systems (IVT)

Microscopic representation of station Ypslikon

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Functional requirements from real-time traffic management

Infrastructure Rolling Stock Operations Macroscopic Microscopic

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Functional requirements from real-time traffic management

Infrastructure Rolling Stock Operations Macroscopic Mesoscopic Microscopic

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Functional requirements from real-time traffic management

Infrastructure Rolling Stock Operations Macroscopic Mesoscopic Microscopic

Functional requirement (Radtke 2014) ”the microscopic infrastructure is not only suitable but even mandatory for exact running time calculation, timetable construction, possession planning and railway operational simulation, conflict detection and resolution.”

Radtke A (2014) Infrastructure modelling. In: Hansen IA, Pachl J (eds) Railway Timetabling and Operations, 2nd edn, Eurail press, Hamburg, Germany, chap 3, pp 47–63.

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Functional requirements from real-time traffic management

Infrastructure Rolling Stock Operations Macroscopic Mesoscopic Microscopic

Functional requirement (Radtke 2014) ”the microscopic infrastructure is not only suitable but even mandatory for exact running time calculation, timetable construction, possession planning and railway operational simulation, conflict detection and resolution.”

Radtke A (2014) Infrastructure modelling. In: Hansen IA, Pachl J (eds) Railway Timetabling and Operations, 2nd edn, Eurail press, Hamburg, Germany, chap 3, pp 47–63.

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

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Example: Speed limits on consecutive sections

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Maximal speed

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Example: Speed limits on consecutive sections

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Maximal speed

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Example: Speed limits on consecutive sections

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Maximal speed Realizable speed

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Example: Speed limits on consecutive sections

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Infrastructure Rolling Stock Operations Maximal speed Realizable speed

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Functional requirements from real-time traffic management

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Infrastructure Rolling Stock Operations Maximal speed Realizable speed Length

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Functional requirements from real-time traffic management

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Infrastructure Rolling Stock Operations Maximal speed Realizable speed Length

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Functional requirements from real-time traffic management

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

Monitoring

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

Monitoring Punctuality

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

Monitoring Punctuality Infrastructure

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

Monitoring Punctuality Infrastructure Rolling Stock

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

Monitoring Punctuality Infrastructure Rolling Stock Staff

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

Monitoring Punctuality Infrastructure Rolling Stock Staff

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Infrastructure Rolling Stock Operations

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Functional requirements from real-time traffic management

Monitoring Punctuality Infrastructure Rolling Stock Staff

Intervention

Functional requirement (Corman and Meng 2013) Actions considered by rescheduling: re-timing an event (e.g. the arrival at or the

departure from a station); re-ordering trains on a shared infrastructure; local re-routing (e.g. platform change); global re-routing; re-servicing.

Corman F, Meng L (2013) A review of online dynamic models and algorithms for railway traffic control. In: Intelligent Rail Transportation (ICIRT), 2013 IEEE International Conference on, pp 128–133, DOI 10.1109/ICIRT.2013.6696281

←Breaking connections, cancelling trains, skipping or adding stops

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Continuous time Event Scheduling Problem (ESP); Alternative Graph (AG); Flexible Path (FP).

Discrete time Arc Packing Problem (APP) and its

weak version (APP’); Path Packing Problem (PPP); Arc Configuration Problem (ACP); Path Configuration Problem (PCP); Resource Tree Conflict Graph

(RTCG) and Tree Conflict Graph (TCG);

Resource Conflict Graph (RCG); REFormulated Simultaneous train

Rerouting and Rescheduling (REF-SRR).

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Mathematical models

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Continuous time Event Scheduling Problem (ESP); Alternative Graph (AG); Flexible Path (FP).

Discrete time Arc Packing Problem (APP) and its

weak version (APP’); Path Packing Problem (PPP); Arc Configuration Problem (ACP); Path Configuration Problem (PCP); Resource Tree Conflict Graph

(RTCG) and Tree Conflict Graph (TCG);

Resource Conflict Graph (RCG); REFormulated Simultaneous train

Rerouting and Rescheduling (REF-SRR).

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Mathematical models

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Continuous time Discrete events: 𝑣𝑣𝑆𝑆𝑧𝑧 Times: 𝑡𝑡𝑆𝑆𝑧𝑧 ≥ 0 Fixed routes

- Train run:

Discrete time

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Mathematical models

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Continuous time Discrete events: 𝑣𝑣𝑆𝑆𝑧𝑧 Times: 𝑡𝑡𝑆𝑆𝑧𝑧 ≥ 0 Fixed routes

- Train run:

Discrete time

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Mathematical models

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐: minimum running time 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐: maximum running time 𝑐𝑐𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷: minimum dwell time 𝑐𝑐𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷: maximum dwell time 𝑐𝑐𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃: earliest time* 𝑐𝑐𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃: latest time 𝑐𝑐𝑂𝑂𝑣𝑣𝐷𝐷𝑂𝑂𝑃𝑃𝐷𝐷𝐷𝐷/ 𝑐𝑐𝑂𝑂𝑣𝑣𝐷𝐷𝑂𝑂𝑃𝑃𝐷𝐷𝐷𝐷 :

minimum/maximum running time from the departure from the first station v to the arrival at destination

* Sometimes referred to as passing constraints

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Continuous time Discrete events: 𝑣𝑣𝑆𝑆𝑧𝑧 Times: 𝑡𝑡𝑆𝑆𝑧𝑧 ≥ 0 Fixed routes

- Train run:

- Interactions

Discrete time

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Mathematical models

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐: minimum connection time 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐: maximum connection time 𝑐𝑐𝐷𝐷𝐷𝐷𝐷𝐷/ 𝑐𝑐𝐷𝐷𝐷𝐷𝐷𝐷 : minimum/maximum

time separation**

** usually defined for ESP only

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ESP

AG

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Mathematical models

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Continuous time Discrete events: 𝑣𝑣𝑆𝑆𝑧𝑧 Times: 𝑡𝑡𝑆𝑆𝑧𝑧 ≥ 0 With routing: 𝑥𝑥𝑆𝑆𝑧𝑧 ∈ {0,1}

Discrete time

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Mathematical models

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-Train run:

-Interactions

Continuous time Discrete events: 𝑣𝑣𝑆𝑆𝑧𝑧 Times: 𝑡𝑡𝑆𝑆𝑧𝑧 ≥ 0 With routing: 𝑥𝑥𝑆𝑆𝑧𝑧 ∈ {0,1}

Discrete time

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Mathematical models

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Continuous time Event Scheduling Problem (ESP); Alternative Graph (AG); Flexible Path (FP).

Discrete time Arc Packing Problem (APP) and its

weak version (APP’); Path Packing Problem (PPP); Arc Configuration Problem (ACP); Path Configuration Problem (PCP); Resource Tree Conflict Graph

(RTCG) and Tree Conflict Graph (TCG);

Resource Conflict Graph (RCG); REFormulated Simultaneous train

Rerouting and Rescheduling (REF-SRR).

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Mathematical models

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Continuous time Event Scheduling Problem (ESP); Alternative Graph (AG); Flexible Path (FP).

Discrete time Arc Packing Problem (APP) and its

weak version (APP’); Path Packing Problem (PPP); Arc Configuration Problem (ACP); Path Configuration Problem (PCP); Resource Tree Conflict Graph

(RTCG) and Tree Conflict Graph (TCG);

Resource Conflict Graph (RCG); REFormulated Simultaneous train

Rerouting and Rescheduling (REF-SRR).

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Mathematical models

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Continuous time Action: 𝑃𝑃 Decision: 𝑥𝑥𝑎𝑎𝑧𝑧 ∈ {0,1}

- Train run: Uniqueness and continuity

Decision for a sequence of actions: 𝑥𝑥𝑝𝑝𝑧𝑧 ∈ {0,1} - Train run: uniqueness:

Discrete time

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Mathematical models

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Continuous time Action: 𝑃𝑃 Decision: 𝑥𝑥𝑎𝑎𝑧𝑧 ∈ {0,1}

- Train run: Uniqueness and continuity

Decision for a sequence of actions: 𝑥𝑥𝑝𝑝𝑧𝑧 ∈ {0,1} - Train run: uniqueness:

Discrete time

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Mathematical models

aStart: departures from the first node;

aEnd: arrivals at the last station; aRun: runs; aDwell: dwells in stations; aInfeasibility: infeasibility

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Continuous time Action: 𝑃𝑃 Decision: 𝑥𝑥𝑎𝑎𝑧𝑧 ∈ {0,1}

- Conflicts

Decision for a sequence of actions: 𝑥𝑥𝑝𝑝𝑧𝑧 ∈ {0,1} - Conflicts:

Discrete time

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Mathematical models

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Mathematical models

PPP

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Meeting functional requirements with mathematical models

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Functional requirements

Matematical Models

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Models that satisfy all the functional requirements identified exist.

Some models are very similar to each others.

Future work: Develop a model for rescheduling starting from the current existing

models, which already satisfy the functional requirements. Take advantage of the similarity with scheduling models that have

fast solving techniques.

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Conclusion and outlook

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Questions?

Thank you for your kind attention!