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Mass transit operators apply operating plans where less frequented stations are not served by all trains, with the aim to shorten the overall passenger travel time. In this paper, we develop two mathematical models in which we explore the possible benefits from two different skipping-stop strategies. In the first model, some stations are skipped by every second train, with the guarantee that every origin-destination pair is feasible without transfer. In the second model, some stations are also skipped by every second train, but without necessarily guaranteeing that every origin-destination pair is feasible without transfer. We adopt here an existing discrete event modeling approach. To have a better overview of the impact of such “skipping stop” policies, we simulate the train dynamics and analyze the skip-stop effects on the service offered to passengers, with our proposed models, and compare the results with those of the case where all trains stop at all stations. The comparison is done in terms of average train frequency and passenger travel time.

Mobil.TUM 2018, International Scientific Conference on Mobility and Transport: Urban Mobility - Shaping the Future Together, MUNICH, ALLEMAGNE, 13-/06/2018 - 14/06/2018; Urban population and mobility needs are rapidly growing while transportation infrastructures are constrained by both limited space and budget allocation. Demand is greater than supply which produces saturation phenomena. Congestion is a major issue impacting the performance of urban transit systems in many ways: operating costs, efficiency and quality of service to name just a few. Regarding rail transit, congestion phenomena are observed in both train and pedestrian traffic. At metro stations, train and pedestrian flows meet and interact with each other. Pedestrian arrivals are pulsed by train arrivals and, inversely, train departures may be delayed because of an excessive number of passengers boarding or/and alighting.The interaction mainly occurs at the platform level where the exchange between passengers is observed.

In this paper we present a mathematical model of the train dynamics in a linear metro line system with demand-dependent 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., Comment: arXiv preprint, accepted for publication at IEEE American Control Conference, Milwaukee, June 2018

We present here a real-time control model for the train dynamics in a linear metro line system. The model describes the train dynamics taking into account average passenger arrival rates on platforms, including control laws for train dwell and run times, based on the feedback of the train dynamics. The model extends a recently developed Max-plus linear traffic model with demand-dependent dwell times and a run time control. The extension permits the elimination of eventual irregularities on the train time-headway. The resulting train dynamics are interpreted as a dynamic programming system of a stochastic optimal control problem of a Markov chain. The train dynamics still admit a stable stationary regime with a unique average growth rate interpreted as the asymptotic average train time-headway. Moreover, beyond the transient regime of the train dynamics, our extension guarantees uniformity in time of the train time-headways at every platform., Version updated on 29/10/2018, index error corrected. arXiv preprint, to appear in Proceedings of the 2018 IEEE Intelligent Transportation Systems Conference, Maui/Hawaii

This paper presents a mathematical model for the train dynamics in a mass-transit metro line system with one symmetrically operated junction. We distinguish three parts: a central part and two branches. The tracks are spatially discretized into segments (or blocks) and the train dynamics are described by a discrete event system where the variables are the $k^{th}$ departure times from each segment. The train dynamics are based on two main constraints: a travel time constraint modeling theoretic run and dwell times, and a safe separation constraint modeling the signaling system in case where the traffic gets very dense. The Max-plus algebra model allows to analytically derive the asymptotic average train frequency as a function of many parameters, including train travel times, minimum safety intervals, the total number of trains on the line and the number of trains on each branch. This derivation permits to understand the physics of traffic. In a further step, the results will be used for traffic control., Comment: 6 pages, 4 figures. arXiv preprint. To be published in Proceedings of 2017 IEEE 56th Conference on Decision and Control (CDC), Melbourne, Australia