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A uni-directional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of car i.e. slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg (Na-Sch) model of traffic flow,…
This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional…
We deal with the problem of deriving the microscopic equations governing the individual car motion based on the assumptions about the strategy of driver behavior. We suppose the driver behavior to be a result of a certain compromise between…
We consider the exclusion process on a ring with time-dependent defective bonds at which the hoping rate periodically switches between zero and one. This system models main roads in city traffics, intersecting with perpendicular streets. We…
This paper devotes to the development of an optimal acceleration/speed profile for autonomous vehicles approaching a traffic light. The design objective is to achieve both short travel time and low energy consumption as well as avoid idling…
We consider a system of ordered cars moving in $\R$ from right to left. Each car is represented by a point in $\R$; two or more cars can occupy the same point but cannot overpass. Cars have two possible velocities: either 0 or 1. An…
Traffic jam in a fluid model of traffic flows proposed by Kerner and Konh\"auser (B. S. Kerner and P. Konh\"auser, Phys. Rev. E 52 (1995), 5574.) is analyzed. An analytic scaling solution is presented near the critical point of the…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
Jamitons are self-sustained traveling wave solutions that arise in certain second-order macroscopic models of vehicular traffic. A necessary condition for a jamiton to appear is that the local traffic density breaks the so-called…
Effects of large value assigned to the maximal car velocity on the fundamental diagrams in the Nagel-Schreckenberg model are studied by extended simulations. The function relating the flow in the congested traffic phase with the car density…
We study driver's optimal trajectory planning under uncertainty in the duration of a traffic light's green phase. We interpret this as an optimal control problem with an objective of minimizing the expected cost based on the fuel use,…
We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow…
We investigate the behaviour of an original traffic model. The model considers a single multi-lane street, populated by autonomous vehicles directed from either end to the other. Lanes have no intrinsic directionality, and the vehicles are…
A two--dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities. Each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of…
We study a model for freeway traffic which includes strong noise taking into account the fluctuations of individual driving behavior. The model shows emergent traffic jams with a self-similar appearance near the throughput maximum of the…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
Traffic congestion has become a nightmare to modern life in metropolitan cities. On average, a driver spending X hours a year stuck in traffic is one of most common sentences we often read regarding traffic congestion. Our aim in this…
We propose a model to implement and simulate different traffic-flow conditions in terms of quantum graphs hosting an ($N$+1)-level dot at each site, which allows us to keep track of the type and of the destination of each vehicle. By…
This paper presents a new approach to congestion management at traffic-light intersections. The approach is based on controlling the relative lengths of red/green cycles in order to have the congestion level track a given reference. It uses…
The increasing wireless communication capabilities of vehicles creates opportunities for more efficient intersection management strategies. One promising approach is the replacement of traffic lights with a system wherein vehicles run…