Traffic modeling and real-time control for metro lines. Part I - A max-plus algebra model explaining the traffic phases of the train dynamics

Farhi, Nadir; Phu, Cyril Nguyen Van; Haj-Salem, Habib; Lebacque, Jean-Patrick

doi:10.23919/acc.2017.7963542

Cited by 17 publications

(47 citation statements)

References 10 publications

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“…For more details on how to model the train dynamics on a metro line in Max-plus algebra and how to technically derive analytic formulas of the average train time-headway and the frequency refer to [4]. The main Theorem we use here to derive the analytic formulas for the average asymptotic train time-headway and frequency is from [3] and has already been applied in [4].…”

Section: Review On Max-plus Algebramentioning

confidence: 99%

Section: Train Dynamicsmentioning

confidence: 99%

“…This work is based on [4] where a discrete event traffic model explaining the traffic phases of the train dynamics on a linear metro line has been proposed. In [4], lower bounds are imposed to the run and dwell times, independent of the passenger travel demand. We extend here the model presented by the authors of [4], accounting for the passenger travel demand in the run and dwell time dynamics.…”

Section: Train Dynamicsmentioning

confidence: 99%

“…In [4], lower bounds are imposed to the run and dwell times, independent of the passenger travel demand. We extend here the model presented by the authors of [4], accounting for the passenger travel demand in the run and dwell time dynamics. As the authors of [4], we consider a space discretization of the metro line into n segments, as shown in Fig.…”

Section: Train Dynamicsmentioning

confidence: 99%

“…Lower and upper bounds are written r j , w j , t j , g j , h j and w j ,t j ,ḡ j ,h j where w j is the minimum dwell time, regarding the demand, and r j the minimum run time, given by the fastest speed profile. The average on k and j of the quantities above are denoted r, w, t, g, h and s. We have the following relationships [4].…”

Section: Train Dynamicsmentioning

confidence: 99%

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A discrete event traffic model explaining the traffic phases of the train dynamics on a linear metro line with demand-dependent control

Schanzenbacher¹,

Farhi

Leurent

et al. 2018

2018 Annual American Control Conference (ACC)

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In this paper we present a mathematical model of the train dynamics in a linear metro line system with demanddependent run and dwell times. On every segment of the line, we consider two main constraints. The first constraint is on the travel time, which is the sum of run and dwell time. The second one is on the safe separation time, modeling the signaling system, so that only one train can occupy a segment at a time. The dwell and the run times are modeled dynamically, with two control laws. The one on the dwell time makes sure that all the passengers can debark from and embark into the train. The one on the run time ensures train time-headway regularity in the case where perturbations do not exceed a run time margin.We use a Max-plus algebra approach which allows to derive analytic formulas for the train time-headway and frequency depending on the number of trains and on the passenger demand. The analytic formulas, illustrated by 3D figures, permit to understand the phases of the train dynamics of a linear metro line being operated as a transport on demand system.

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Section: Review On Max-plus Algebramentioning

confidence: 99%

Section: Train Dynamicsmentioning

confidence: 99%