Related papers: Stationary analysis of certain Markov-modulated re…
We consider a Markov modulated fluid network with a finite number of stations. We are interested in the tail asymptotics behavior of the stationary distribution of its buffer content process. Using two different approaches, we derive upper…
Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set of boundary states and a structured…
This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The…
For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of M\"obius monotonicity of the chain. We show relations of M\"obius monotonicity to other definitions of monotone chains.…
In queuing theory and related problems, it is very important to know the numerical characteristics of an investigated system - both in stationary and non-stationary modes. In some cases, such characteristics can be calculated, but this is…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
What can one say on convergence to stationarity of a finite state Markov chain that behaves "locally" like a nearest neighbor random walk on ${\mathbb Z}$ ? The model we consider is a version of nearest neighbor lazy random walk on the…
The bike sharing systems are fast increasing as a public transport mode in urban short trips, and have been developed in many major cities around the world. A major challenge in the study of bike sharing systems is that large-scale and…
We analyze the stationary distribution of regulated Markov modulated Brownian motions (MMBM) modified so that their evolution is slowed down when the process reaches level zero --- level zero is said to be {\em sticky}. To determine the…
Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their…
We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…
We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be…
This paper studies the queue length process in series Jackson networks with external input to the first station. We show that its Markov transition probabilities can be written as a finite sum of non-crossing probabilities, so that…
Quantum repeater chains will form the backbone of future quantum networks that distribute entanglement between network nodes. Therefore, it is important to understand the entanglement distribution performance of quantum repeater chains,…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or…
We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…
In this note, a general approach to the study of non-stationary Markov chains with catastrophes and the corresponding queuing models is considered, as well as to obtain estimates of the limiting regime itself. As an illustration, an example…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…