Related papers: Traffic Light Queues and the Poisson Clumping Heur…
We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a…
A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…
This paper presents a mathematical model for the train dynamics in a mass-transit metro line system with one symmetrically operated junction. We distinguish three parts: a central part and two branches. The tracks are spatially discretized…
Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
We investigate a traffic model in which cars either move freely with quenched intrinsic velocities or belong to clusters formed behind slower cars. In each cluster, the next-to-leading car is allowed to pass and resume free motion. The…
This paper tackles the challenge of coordinating traffic lights and automated vehicles at signalized intersections, formulated as a constrained finite-horizon optimal control problem. The problem falls into the category of mixed-integer…
We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing…
We consider random temporal graphs, a version of the classical Erd\H{o}s--R\'enyi random graph G(n,p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time…
We study the distances of edges within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away points are less likely to be connected than nearby points. We…
The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…
We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on the bus is fixed. The customers arriving at station i wait for…
The article studies the almost surely asymptotics of extreme values $\bar{\xi}_n = \max_{1\leq i \leq n} \xi_i$, where $ \xi , \xi_1 , \xi_2 , \ldots$ are discrete identically distributed random variables. One of the main results on this…
In this first paper of a series of two we are going to show that, on the ground of few reasonable hypotheses, an equation linking the number of vehicle N($\tau_i$), that run from (i-1)-th to the i-th hour, to the ground-level hourly average…
We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen (1998), simplify its proof,…
If a line cuts randomly two sides of a triangle, the length of the segment determined by the points of intersection is also random. The object of this study, applied to a particular case, is to calculate the probability that the length of…
The present paper proposes a stochastic model of the traffic flow. This model has a discrete set of states and the continuous time. The model is a generalization of the discrete stochastis model that has been considered in a previous paper…
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with…
We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the…
Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce.…