Nadir Farhi

Nadir Farhi, Maurice Goursat, Jean-Pierre Quadrat

We study the relation between the average traffic flow and the vehicle density on road networks that we call 2D-traffic fundamental diagram. We show that this diagram presents mainly four phases. We analyze different cases. First, the case of a junction managed with a priority rule is presented, four traffic phases are identified and described, and a good analytic approximation of the fundamental diagram is obtained by computing a generalized eigenvalue of the dynamics of the system. Then, the model is extended to the case of two junctions, and finally to a regular city. The system still presents mainly four phases. The role of a critical circuit of non-priority roads appears clearly in the two junctions case. In Section 4, we use traffic light controls to improve the traffic diagram. We present the improvements obtained by open-loop, local feedback, and global feedback strategies. A comparison based on the response times to reach the stationary regime is also given. Finally, we show the importance of the design of the junction. It appears that if the junction is enough large, the traffic is almost not slowed down by the junction.

Nadir Farhi

We present a traffic model that extends the linear car-following model as well as the min-plus traffic model (a model based on the min-plus algebra). A discrete-time car-dynamics describing the traffic on a 1-lane road without passing is interpreted as a dynamic programming equation of a stochastic optimal control problem of a Markov chain. This variational formulation permits to characterize the stability of the car-dynamics and to calculte the stationary regimes when they exist. The model is based on a piecewise linear approximation of the fundamental traffic diagram.

Cyril Nguyen Van Phu, Nadir Farhi

We present in this paper a method to estimate urban traffic state with communicating vehicles. Vehicles moving on the links of the urban road network form queues at the traffic lights. We assume that a proportion of vehicles are equipped with localization and communication capabilities, and name them probe vehicles. First, we propose a method for the estimation of the penetration ratio of probe vehicles, as well as the vehicles arrival rate on a link. Moreover, we show that turn ratios at each junction can be estimated. Second, assuming that the turn ratios at each junction are given, we propose an estimation of the queue lengths on a 2-lanes link, by extending a 1-lane existing method. Our extension introduces vehicles assignment onto the lanes. Third, based on this approach, we propose optimal control laws for the traffic light and for the assignment of the arriving vehicles onto the lane queues. Finally, numerical simulations are conducted with Veins framework that bi-directionally couples microscopic road traffic and communication simulators. We illustrate and discuss our propositions with the simulation results.

Nadir Farhi

In this work, we address the problem of determining reliable policies in reinforcement learning (RL), with a focus on optimization under uncertainty and the need for performance guarantees. While classical RL algorithms aim at maximizing the expected return, many real-world applications - such as routing, resource allocation, or sequential decision-making under risk - require strategies that ensure not only high average performance but also a guaranteed probability of success. To this end, we propose a novel formulation in which the objective is to maximize the probability that the cumulative return exceeds a prescribed threshold. We demonstrate that this reliable RL problem can be reformulated, via a state-augmented representation, into a standard RL problem, thereby allowing the use of existing RL and deep RL algorithms without the need for entirely new algorithmic frameworks. Theoretical results establish the equivalence of the two formulations and show that reliable strategies can be derived by appropriately adapting well-known methods such as Q-learning or Dueling Double DQN. To illustrate the practical relevance of the approach, we consider the problem of reliable routing, where the goal is not to minimize the expected travel time but rather to maximize the probability of reaching the destination within a given time budget. Numerical experiments confirm that the proposed formulation leads to policies that effectively balance efficiency and reliability, highlighting the potential of reliable RL for applications in stochastic and safety-critical environments.

Romain Ducrocq, Nadir Farhi

Intelligent traffic signal controllers, applying DQN algorithms to traffic light policy optimization, efficiently reduce traffic congestion by adjusting traffic signals to real-time traffic. Most propositions in the literature however consider that all vehicles at the intersection are detected, an unrealistic scenario. Recently, new wireless communication technologies have enabled cost-efficient detection of connected vehicles by infrastructures. With only a small fraction of the total fleet currently equipped, methods able to perform under low detection rates are desirable. In this paper, we propose a deep reinforcement Q-learning model to optimize traffic signal control at an isolated intersection, in a partially observable environment with connected vehicles. First, we present the novel DQN model within the RL framework. We introduce a new state representation for partially observable environments and a new reward function for traffic signal control, and provide a network architecture and tuned hyper-parameters. Second, we evaluate the performances of the model in numerical simulations on multiple scenarios, in two steps. At first in full detection against existing actuated controllers, then in partial detection with loss estimates for proportions of connected vehicles. Finally, from the obtained results, we define thresholds for detection rates with acceptable and optimal performance levels.

Cyril Nguyen Van Phu, Nadir Farhi, Habib Haj-Salem et al.

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.