Related papers: T\'oth's buses and the "detachment process''
Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…
We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state…
Using a microscopic model for stochastic transport through a single quantum dot that is modified by the Coulomb interaction of environmental (weakly coupled) quantum dots, we derive generic properties of the full counting statistics for…
This paper is devoted to the study of the number of customers in infinite-server systems driven by Hawkes processes. In these systems, the self-exciting arrival process is assumed to be represented by a Hawkes process and the self-exciting…
Disruptions are an inherent feature of transportation systems, occurring unpredictably and with varying durations. Even after an incident is reported as resolved, disruptions can induce irregular train operations that generate substantial…
Consider $n$ independent Goldstein-Kac telegraph processes $X_1(t), \dots ,X_n(t), \; n\ge 2, \; t\ge 0,$ on the real line $\Bbb R$. Each the process $X_k(t), \; k=1,\dots,n,$ describes a stochastic motion at constant finite speed $c_k>0$…
We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and…
A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by…
We consider a stationary Markov process that models certain queues with a bulk service of a fixed number $m$ of admitted customers. We find an integral expression of its transition probability function in terms of certain multi-orthogonal…
This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite state Markov process that modulates the…
Recently, an Enskog-type kinetic theory for Vicsek-type models for self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901 (2011)]. This theory is based on an exact equation for a Markov chain in phase space and is not…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
Accurate forecasting of bus travel time and its uncertainty is critical to service quality and operation of transit systems; for example, it can help passengers make better decisions on departure time, route choice, and even transport mode…
Bus bunching is a curse of transportation systems such as buses in a loop. Here we present an analytical method to find the number of revolutions before two buses bunch in an idealised system, as a function of the initial distance and the…
An analysis of transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces is presented. The synchronization phenomenon is investigated in the ensemble of particles moving…
In this paper we present a mathematical model of the train dynamics in a linear metro line system with demand-dependent run and dwell times. On every segment of the line, we consider two main constraints. The first constraint is on the…
We consider the Markov random flight $\bold X(t), \; t>0,$ in the three-dimensional Euclidean space $\Bbb R^3$ with constant finite speed $c>0$ and the uniform choice of the initial and each new direction at random time instants that form a…
We consider the problem of `discrete-time persistence', which deals with the zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no…
Providing transport users and operators with accurate forecasts on travel times is challenging due to a highly stochastic traffic environment. Public transport users are particularly sensitive to unexpected waiting times, which negatively…
An infinite buffer batch service vacation queue has been studied where service rate of the batch is dependent on the size of the batch and vacation rate is dependent on the queue size at vacation initiation epoch. The arrivals follow the…