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The paper is devoted to the estimation of the rate of of exponential convergence of nonhomogeneous queues exhibiting different types of ergodicity. The main tool of our study is the method, which was proposed by the second author in the…

Probability · Mathematics 2007-06-13 Boris L. Granovsky , Aleksandr I. Zeifman

In this paper, we consider a $G_t/G_t/\infty$ infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account…

Probability · Mathematics 2020-04-13 Harsha Honnappa , Yiran Liu , Samy Tindel , Aaron Yip

This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…

Probability · Mathematics 2007-05-23 George Yin , Hanqin Zhang

We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means…

Probability · Mathematics 2019-07-15 Ari Arapostathis , Anirban Das , Guodong Pang , Yi Zheng

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…

Probability · Mathematics 2018-12-05 F. Baccelli , A. Rybko , S. Shlosman , A. Vladimirov

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…

Probability · Mathematics 2015-10-02 Jori Selen , Ivo J. B. F. Adan , Johan S. H. van Leeuwaarden

In this paper we study the Markov-modulated M/M/$\infty$ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system's asymptotic behavior under a particular scaling of the…

Probability · Mathematics 2016-01-13 Joke Blom , Koen de Turck , Michel Mandjes

We consider a two-node queue modeled as a two-dimensional random walk. In particular, we consider the case that one or both queues have finite buffers. We develop an approximation scheme based on the Markov reward approach to error bounds…

Probability · Mathematics 2020-10-28 Yanting Chen , Xinwei Bai , Richard J. Boucherie , Jasper Goseling

In this paper, we analyze a retrial queueing system with Batch Markovian Arrival Processes and two types of customers. The rate of individual repeated attempts from the orbit is modulated according to a Markov Modulated Poisson Process.…

Probability · Mathematics 2015-04-07 Jinbiao Wu , Yi Peng , Zaiming Liu

The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are…

Probability · Mathematics 2022-12-27 Aleksandr Shchegolev

We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…

Networking and Internet Architecture · Computer Science 2019-07-26 Iqra Altaf Gillani , Amitabha Bagchi , Pooja Vyavahare

We investigate a processor sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue, or renege, before completing service. The corresponding stochastic processes are represented by…

Probability · Mathematics 2009-08-25 Christian H. Gromoll , Philippe Robert , Bert Zwart

We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…

Probability · Mathematics 2011-05-04 David Gamarnik , Alexander Stolyar

We consider a tandem queue with coupled processors, which is subject to global breakdowns. When the network is in the operating mode and both queues are non empty, the total service capacity is shared among the stations according to fixed…

Probability · Mathematics 2019-03-08 Ioannis Dimitriou

In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another.…

Probability · Mathematics 2024-11-26 Mohammad Daneshvar , Richard C. Barnard , Cory Hauck , Ilya Timofeyev

We consider an infinite server queue where the arrival and the service rates are both modulated by a stochastic environment governed by an $S$-valued stochastic process $X$ that is ergodic with a limiting measure $\pi\in \mathcal{P}(S)$.…

Probability · Mathematics 2024-10-30 Abhishek Pal Majumder

We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and…

Probability · Mathematics 2018-01-19 Abhishek , Marko Boon , Onno Boxma , Rudesindo Núñez-Queija

A heterogeneous closed network with one-server queues with finite capacity and one infinite-server queue is studied. A target application is bike-sharing systems. Heterogeneity is taken into account through clusters whose queues have the…

Adaptation and Self-Organizing Systems · Physics 2014-05-26 Christine Fricker , Nicolas Servel

In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other…

Probability · Mathematics 2023-08-01 Pierre Popineau , Seva Shneer

The paper analyzes the performance of tandem network of polling queue with setups. For a system with two-products and two-stations, we propose a new approach based on a partially-collapsible state-space characterization to reduce…

Performance · Computer Science 2022-02-22 Ravi Suman , Ananth Krishnamurthy