Marie Skłodowska-Curie Actions

MSCA-COFUND-CLEAR-Doc-PhD Position #CD22-28: Analytic traffic modeling and control on a mass transit network including passenger flows

    Université Gustave Eiffel
    Computer science
    MathematicsApplied mathematics
    First Stage Researcher (R1)
    31/01/2023 17:00 - Europe/Brussels
    France › Marne-La-Vallée
    H2020 / Marie Skłodowska-Curie Actions COFUND


Rail-bound transport systems such as subways or metros are the backbone of public transport in urban areas and mega cities. They provide a high level of passenger capacity and transport efficiency, and typically operate on specific tracks and lines in order to ensure high operating frequency and service quality. Given the limited routing flexibility and dense operation of trains, corresponding mass transit systems are susceptible to operational perturbations, resulting from, e.g., excessive station dwell times due to train or platform crowding. To optimally control and provide a high reliability of train operations, a detailed understanding of the behavior and performance of the transport system is required. To this end, advanced mathematical modelling techniques allowing to assess the inter-dependencies of trains are vital in providing decision support to traffic planning and management. This PhD project, which is co-located at Grettia laboratory of Univ. Gustave Eiffel and the DLR – Institute of Transportation Systems in Brunswick, Germany, aims to extend and improve existing modelling techniques to improve the quality of information available to rail traffic planners.


The objective of this thesis is to extend an existing algebraic approach for traffic modeling on isolated loop metro lines, to traffic modeling and control on a network of metros and mass transit lines. Several extensions will be considered:

1. Account for stochastic effects in relation to passenger boarding / alighting behavior and corresponding train station dwell times.

2. Isolated metro lines will be connected based on the flow of passengers in transfer stations. Starting from small networks with two or three lines, models with an increasing number of metro lines will be considered.

3. Finally, passenger flow assignment will be considered. Data on the passenger travel demand can be available thanks to a collaboration with RATP (the metro line operator Paris).

Methodology and related works:

In this thesis, we propose to consider an algebraic approach for modelling the train dynamics in metro lines, which can be used both in a deterministic and stochastic setting allowing to incorporate different kinds of uncertainties, in particular concerning the passenger flow dynamics. The passenger traffic assignment is to be introduced using equilibrium and optimization models to models based on the operating status of the network. Concerning the algebraic approach for the train dynamics, the first traffic model was proposed in [1]. It is a Max-plus algebra model for the train dynamics on a loop metro line, where lower bounds for train run, dwell and safe-separation times are considered. This model permitted analytical derivation of what is called fundamental traffic diagrams (giving the train frequency as a function of the number of running trains). One of the most recent extension of this model was the one in [2], where the passenger travel demand has been considered (flows by origin-destination) and where passenger capacities of trains as well as passenger comfort inside the trains have been considered.

The current approaches for optimal control of metro systems discussed before rely on line-specific, deterministic modelling of train operations and passenger flows (cf. [1]) based on a mean-value approach. At the same time, it is well-known that variability of input parameters and the associated stochastic effects have a significant effect on the system performance (cf. [3]). The statistics of station dwell times notably depends on the level of crowding on station platforms and the passenger transfer processes between different lines, and hence, the network situation. To this end, (max,+)-models with stochastic input have been developed [4, 5, 6] and used to assess the stability and robustness of timetables in view of disruptions and input data variability. In this work, train control and traffic assessment in the deterministic case are to be extended by stochastic modelling of passenger flows and station dwell times, and transferability and limitations of modelling and solution approaches are assessed.

Challenges and Impact:

The work we propose here can have impacts on many pressing problems in railway operations on urban mass-transit networks:

- First, in terms of traffic modeling on mass transit lines, it consists in proposing realistic traffic models taking into account uncertainty and its role in the effective system performance.

- Second, it provides an integrated modeling perspective on train traffic and passenger flows including inter-dependencies between the network traffic situation and the passengers’ route choice and the assignment and reassignment of itineraries on the network.

As the work deals with intricate (possibly cyclic) dependencies within a network, it bears several major research and modelling challenges.

- The extension of existing deterministic traffic models to stochastic ones is one of the main challenges, in the sense that the main uncertainties on the traffic dynamics need to be characterized and modeled in a way which would permit a good comprehension of the traffic.

- Effective optimization models for the passenger flow assignments on the network are to be developed in order to allow the operators of the transit networks to control and regulate the passenger flows.

- Finally, a consistent coupling of the passenger flow assignment and the train dynamics modelling is required, which allows to assess passenger assignment and re-assignment based on the current network operation state.


[1] N. Farhi et al. Traffic modeling and real-time control for metro lines, IEEE ACC, 2017.

[2] N. Farhi, A discrete-event model of the train traffic on a linear metro line, Applied Math. Modelling 2021.

[3] N. Weik and N. Nießen, Quantifying the effects of running time variability on the capacity of rail corridors, Journal of Rail Transport Planning & Management, 2020.

[4] T. Büker and B. Seybold, Stochastic modelling of delay propagation in large networks, Journal of Rail Transport Planning & Management, 2012.

[5] R. Goverde, B. Heidergott and G. Merlet, Railway Timetable Stability Analysis Using Stochastic Max-Plus Linear Systems, in 3rd International Seminar on Railway Operations Modelling and Analysis, Zurich, 2009.

[6] A. de Kort, B. Heidergott and H. Ayhan, A probabilistic (max,+) approach for determining railway infrastructure capacity, European Journal of Op. Research, 2003.

More Information


  • High-quality doctoral training rewarded by a PhD degree, delivered by Université Gustave Eiffel
  • Access to cutting-edge infrastructures for research & innovation
  • Appointment for a period of 36 months based on a salary of 2 700 € (gross salary per month)
  • Job contract under the French labour legislation in force, respecting health and safety, and social security: 35 hours per week contract, 25 days of annual leave per year
  • International mobility will be mandatory
  • An international environment supported by the adherence to the European Charter & Code
  • Access to dedicated CLEAR-Doc trainings with a strong interdisciplinary focus, together with a Career development Plan

Eligibility criteria

Applicants must fulfil the following eligibility criteria :

  • At the time of the deadline, applicants must be in possession or finalizing their Master’s degree or equivalent/postgraduate degree
  • At the time of recruitment, applicants must be in possession of their Master’s degree or equivalent/postgraduate degree which would formally entitle to embark on a doctorate
  • At the time of the deadline, applicants must be in the first four years (full-time equivalent research experience) of their research career (career breaks excluded) and not yet been awarded a doctoral degree. Career breaks refer to periods of time where the candidate was not active in research, regardless of his/her employment status (sick leave, maternity leave etc). Short stays such as holidays and/or compulsory national service are not taken into account
  • At the time of the deadline, applicants must fulfil the transnational mobility rule: incoming applicants must not have resided or carried out their main activity (work, studies, etc.) in France for more than 12 months in the 3 previous years
  • One application per call per year is allowe
  • Applicants must be available full-time to start the programme on schedule (November 1st 2023)
  • Application rules are enforced by the French doctoral system which specifies a standard duration of 3 years for a full-time PhD together with the MSCA standards and the OTM-R European rules as follows
  • Citizens of any nationality may apply to the programme
  • There is no age limit

Selection process

Additional comments

  • The first step before applying is contacting the PhD supervisor. You will not be able to apply without an acceptation letter from the PhD supervisor
  • International mobility planned : International mobility planned at teh German Aerospace Center-DLR (Germany)
  • Please contact the PhD supervisor for any additional detail on job offer
  • There are no restrictions concerning the age, gender or nationality of the candidates. Applicants with career breaks or variations in the chronological sequence of their career, with mobility experience or with interdisciplinary background or private sector experience are welcome to apply
  • Support service is available during every step of the application process by email: clear-doc@univ-eiffel.fr

Web site for additional job details

Offer Requirements

    Mathematics: Master Degree or equivalent
    Computer science: Master Degree or equivalent
    Physics: Master Degree or equivalent
    Engineering: Master Degree or equivalent
    FRENCH: Basic
    ENGLISH: Excellent


  • At the time of the deadline, applicants must be in possession or finalizing their Master’s degree or equivalent/postgraduate degree.
  • At the time of recruitment, applicants must be in possession of their Master’s degree or equivalent/postgraduate degree which would formally entitle to embark on a doctorate.

Map Information

Job Work Location Personal Assistance locations
Work location(s)
1 position(s) available at
Université Gustave Eiffel
5, Boulevard Descartes

EURAXESS offer ID: 846821


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