Related papers: Conjectures about Traffic Light Queues
We give a simple derivation of the distribution of the maximum L of the length of the queue during a busy period for the M/M/1 queue with lambda<1 the ratio between arrival rate and service rate. We observe that the asymptotic behavior of…
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…
For autonomous vehicles to safely share the road with human drivers, autonomous vehicles must abide by specific "road rules" that human drivers have agreed to follow. "Road rules" include rules that drivers are required to follow by law --…
Based on numerical simulations of a three-phase traffic flow model, a probabilistic theory of traffic at the light signal is developed. We have found that very complex spatiotemporal self-organized phenomena determine features of city…
We study the Traffic Light Control (TLC) problem for a single intersection, considering both straight driving vehicle flows and corresponding crossing pedestrian flows with the goal of achieving a fair jointly optimal sharing policy in…
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
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…
We consider a horizontal traffic queue (HTQ) on a periodic road segment, where vehicles arrive according to a spatio-temporal Poisson process, and depart after traveling a distance that is sampled independently and identically from a…
We investigate the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p…
As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation…
The placement and dimensioning of exit routes is informed by experimental data and theoretical models. The experimental data is still to a large extent uncertain and contradictory. In this contribution an attempt is made to understand and…
Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ with increments $(1,0)$, $(-1,0)$, $(0,1)$ and $(0,-1)$; $X$ represents, at arrivals and service completions, the lengths of two queues working in parallel whose service and…
Modern networks exhibit a high degree of variability in link rates. Cellular network bandwidth inherently varies with receiver motion and orientation, while class-based packet scheduling in datacenter and service provider networks induces…
We introduced a probability of traffic light, PL, at an intersection when approaching cars in two roads are in same conditions. As a application, we proposed a modified Nagel-Schreckenberg cellular automata model for describing a…
With autonomous vehicles now sharing roads with human drivers, the era of mixed autonomy brings new challenges in dealing with congestion. One cause of congestion is when vehicle users choose their routes selfishly to minimize their…
We say that a random variable is $light$-$tailed$ if moments of order $2+\epsilon$ are finite for some $\epsilon>0$; otherwise, we say that it is $heavy$-$tailed$. We study queueing networks that operate under the Max-Weight scheduling…
We show that the capacity of a complex network that models a city street grid to support congested traffic can be optimized by using routes that collectively minimize the maximum ratio of betweenness to capacity in any link. Networks with a…
We consider multi-component matching systems in heavy traffic consisting of $K\geq 2$ distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues…
During the attempt to line up into a dense traffic people have necessarily to share a limited space under turbulent conditions. From the statistical point view it generally leads to a probability distribution of the distances between the…
Fair queuing is becoming increasingly prevalent in the internet and has been shown to improve performance in many circumstances. Performance could be improved even more if endpoints could detect the presence of fair queuing on a certain…