Related papers: Traffic lights, clumping and QBDs

In discrete time, customers arrive at random. Each waits until one of three servers is available; each thereafter departs at random. We seek the distribution of maximum line length of idle customers. Algebraic expressions obtained for the…

The traffic flow through a light signal is explored by using the optimal velocity model and its improvement known as full velocity differences model. The simulations consider a single line of identical cars, equally spaced, and with no…

Based of simulations of a stochastic three-phase traffic flow model, we reveal that at a signalized city intersection under small link inflow rates at which a vehicle queue developed during the red phase of light signal dissolves fully…

Setting traffic light signals is a classical topic in traffic engineering, and important in heavy-traffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an…

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…

Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each…

We describe traffic flows in one lane roadways using kinetic theory, with special emphasis on the role of quenched randomness in the velocity distributions. When passing is forbidden, growing clusters are formed behind slow cars and the…

We consider two variations of the discrete car parking problem where at every vertex of the integers a car arrives with rate one, now allowing for parking in two lines. a) The car parks in the first line whenever the vertex and all of its…

We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic…

This article mediates an mathematical insight to the theory of vehicular headways measured on signalized crossroads. Considering both, mathematical and empirical substances of the socio-physical system studied, we firstly formulate several…

In discrete time, customers arrive at random. Each waits until one of two servers is available; each thereafter departs at random. We seek the distribution of maximum line length of idle customers. In the context of an emergency room (for…

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…

Traffic congestion games abstract away from the costs of junctions in transport networks, yet, in urban environments, these often impact journey times significantly. In this paper we equip congestion games with traffic lights, modelled as…

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…

Asymptotic properties of random regular graphs are object of extensive study in mathematics. In this note we argue, based on theory of spin glasses, that in random regular graphs the maximum cut size asymptotically equals the number of…

We study the asymptotic behavior of cycles of uniformly random parking functions. Our results are multifold: we obtain an explicit formula for the number of parking functions with a prescribed number of cyclic points and show that the…

Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…

We present a microscopic driving algorithm that prescribes the acceleration using three parameters: the distance to the leading vehicle, to the next traffic light and to the nearest stopping point when the next traffic light is in the red…

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…

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,…