Related papers: Traffic Light Queues and the Poisson Clumping Heur…

Let $k,d $ be positive integers. We determine a sequence of constants that are asymptotic to the probability that the cluster at the origin in a $d$-dimensional Poisson Boolean model with balls of fixed radius is of order $k$, as the…

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…

While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…

This paper develops a framework to study multi-hop relaying in a vehicular network consisting of vehicles and Road Side Units (RSUs), and the effect of this relaying on the network coverage and the communication delay. We use a stochastic…

In this paper, we study the stability of light traffic achieved by a scheduling algorithm which is suitable for heterogeneous traffic networks. Since analyzing a scheduling algorithm is intractable using the conventional mathematical tool,…

We study local features, and provide a topological insight into the global structure of the probability density distribution and of the pattern of the optimal paths for large rare fluctuations away from a stable state. In contrast to…

We determine the probability thresholds for the existence of monotone paths, of finite and infinite length, in random oriented graphs with vertex set $\mathbb N^{[k]}$, the set of all increasing $k$-tuples in $\mathbb N$. These graphs…

A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian limit theorem is proved for the position of a particle in the…

We introduce and study several random combinatorial billiard trajectories. Such a system, which depends on a fixed parameter $p\in(0,1)$, models a beam of light that travels in a Euclidean space, occasionally randomly reflecting off of a…

Forecasting trajectories of human-driven vehicles is a crucial problem in autonomous driving. Trajectory forecasting in the urban area is particularly hard due to complex interactions with cars and pedestrians, and traffic lights (TLs).…

Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…

In previous papers, threshold probabilities for the properties of a random distance graph to contain strictly balanced graphs were found. We extend this result to arbitrary graphs and prove that the number of copies of a strictly balanced…

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

We consider a discrete time parallel queue, which is two-queue network, where at each time-slot there is a the same batch arrival to both queues and at each queue there is a random service available. The service law at each time-slot for…

We prove the law of large numbers for the drift of random walks on the two-dimensional lamplighter group, under the assumption that the random walk has finite $(2+\epsilon)$-moment. This result is in contrast with classical examples of…

In a circuit-switched network, traffic can be characterized by several factors that define how communication resources are allocated and utilized during a connection. The amount of traffic basically determines how frequently connection…

We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…

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…

We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin.…

We present a flow-control technique in traffic-light intersections, aiming at regulating queue lengths to given reference setpoints. The technique is based on multivariable integrators with adaptive gains, computed at each control cycle by…