Nadir Farhi

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

We present in this article a traffic flow model for metro lines. It is a discrete event model written in the max-plus algebra, where the traffic dynamics take into account time constraints such as minimum train inter-station running times, minimum train dwell times on platforms, and minimum safety times between successive trains. We show that the dynamics admit a unique stable stationary regime. Moreover, the asymptotic average train time-headway, dwell time, as well as safe-separation time, are derived analytically, as functions of the number of moving trains on the metro line. This derivation allows the comprehension of the traffic phases of the train dynamics.

M/G/c/c state dependent queuing model for a road traffic system of two sections in tandem

We propose in this article a M/G/c/c state dependent queuing model for road traffic flow. The model is based on finite capacity queuing theory which captures the stationary density-flow relationships. It is also inspired from the deterministic Godunov scheme for the road traffic simulation. We first present a reformulation of the existing linear case of M/G/c/c state dependent model, in order to use flow rather than speed variables. We then extend this model in order to consider upstream traffic demand and downstream traffic supply. After that, we propose the model for two road sections in tandem where both sections influence each other. In order to deal with this mutual dependence, we solve an implicit system given by an algebraic equation. Finally, we derive some performance measures (throughput and expected travel time). A comparison with results predicted by the M/G/c/c state dependent queuing networks shows that the model we propose here captures really the dynamics of the road traffic.

On the robust guidance of users in road traffic networks

We present in this article a model for the guidance of users in raod traffic networks. It is well known since decades that a path with a reliable travel time can be obtained by maximizing, over the different possible paths, the probability of realizing a travel time less than a given time budget. We propose here an adaptation of this approach, in order to introduce robustness in the selection of the optimal path. A robust path here is a path that is not likely to change during the travel, and that admits acceptable alternative detours in case of failure.

Risk Index Model Building

Abstract This paper aims at developing a risk index based on real-data measurements, which can be used either off-line as an evaluation index during the evaluation process which leads to the dramatical reduction of the field test periods, or in real-time like: a safety monitoring tool (e.g. safety user warning system), or a multi-criterion function to be optimized in real time (safety index combined with a traffic index) within several control strategies, such as coordinated ramp metering, speed limit control, route guidance, etc.

A vehicle-to-infrastructure communication based algorithm for urban traffic control

We present in this paper a new algorithm for urban traffic light control with mixed traffic (communicating and non communicating vehicles) and mixed infrastructure (equipped and unequipped junctions). We call equipped junction here a junction with a traffic light signal (TLS) controlled by a road side unit (RSU). On such a junction, the RSU manifests its connectedness to equipped vehicles by broadcasting its communication address and geographical coordinates. The RSU builds a map of connected vehicles approaching and leaving the junction. The algorithm allows the RSU to select a traffic phase, based on the built map. The selected traffic phase is applied by the TLS; and both equipped and unequipped vehicles must respect it. The traffic management is in feedback on the traffic demand of communicating vehicles. We simulated the vehicular traffic as well as the communications. The two simulations are combined in a closed loop with visualization and monitoring interfaces. Several indicators on vehicular traffic (mean travel time, ended vehicles) and IEEE 802.11p communication performances (end-to-end delay, throughput) are derived and illustrated in three dimension maps. We then extended the traffic control to a urban road network where we also varied the number of equipped junctions. Other indicators are shown for road traffic performances in the road network case, where high gains are experienced in the simulation results.

Traffic modeling and real-time control for metro lines. Part II - The effect of passenger demand on the traffic phases

We present traffic flow and control models for the train dynamics in metro lines. In a first model we introduce the effect of passenger demand on the train dwell times at platforms. We recall that, if this effect is not well controlled, then the traffic is unstable. Then we propose a second traffic control model which deals with this instability, by modifying the control of the train dwell times at platforms. We show that the dynamic system admits a unique stable asymptotic regime, and calculate by numerical simulations the asymptotic average train time-headway as a function of the number of moving trains. By that, we obtain the traffic phases of the train dynamics, giving the effect of the passenger travel demand on the frequency of the metro line, under the proposed control model. Finally, we draw some conclusions, and give a direction for the upcoming research.

An Algorithm for Robust Routing Strategies in Networks

In this article, the authors address the problem of optimal guidance of road network users. In the literature, several routing algorithms have been proposed under different approaches to solve this problem. Most adaptive algorithms for optimal path are based on the least expected travel time. Another approach has emerged named the SOTA (stochastic on time arrival). This approach based on the idea of Frank (1969), which aims to maximize the probability of arriving to a destination node parting from a given node in the network and with a given time budget. The authors’ contribution consists here in extending this approach in order to introduce robustness towards path failure, in the guidance optimization. The authors propose a model that includes the existence as well as the performance of detours for selected paths, in the calculus of the travel time reliability. This new way of calculating travel time reliability guarantees a kind of robustness of the optimal guidance strategy.

Managing planned disruptions of mass transit systems

Unplanned disruptions of rail transit networks have been studied extensively. Planned disruptions for works essentially are different mainly because of their longer duration, which allows passengers to build alternative route choice strategies. The literature on this topic remains scarce. In this study, a novel methodology was proposed to enable operators to evaluate different disruption management schemes and to obtain explicit estimations of travel times, passenger comfort flows, and levels of service. Statistical tools were used to evaluate the different strategies. The methodology is illustrated here through a large-scale application to a real line disruption in Paris. The disruption took place in July 2015 as the result of network maintenance work and affected Line A of Réseau Express Régional, a major suburban railway line that provides more than 1 million trips on a typical working day. Study results indicated that the disruption would have significantly increased the generalized cost (GC) of passengers if no action had been taken. The operator’s disruption management scheme included bus bridging and increases in service frequency on alternative routes. Evaluation showed that this plan restored the average GC across the whole network. Passengers who initially used the disrupted line experienced increased GC when they used the longer, alternative routes. Passengers who initially used those alternative routes experienced lower GC as a result of the increase in service frequency. Finally, capacity problems were observed on the buses that ensured a bridge across the disrupted link.

Development of Coordinated Ramp-Metering Based on Multi-objective Nonlinear Optimization Functions: Traffic and Safety

This paper is focused on the extension of the OASIS (Optimal Advanced System for Integrated Strategies) in order to take into account the multi-objective nonlinear optimization technique for coordinated ramp metering. The multi-objective function includes two costs functions: traffic and safety (Risk model) indices. OASIS is revisited and off-line simulation studies are conducted on real test site corresponding to A6W France motorway located in the south part of “Ile de France” Motorway networks. Five consecutive on-ramps are considered for the control. The obtained results are very promising.

Preface of the “Symposium on modeling, simulation and optimization of transportation networks”

This session of ICNAAM is devoted to traffic flow modeling, simulation and optimization in transportation networks. Thirteen long abstracts have been selected for presentation at ICNAAM 2014 in Rhodes, based on a peer review process. However most of the selected articles treat traffic models for road networks, three streams are distinguished in the whole work of the contributions: A - traffic modeling, B- traffic simulation, and C- traffic control.