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Related papers: Perfect Sampling of GI/GI/c Queues

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This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The…

Probability · Mathematics 2009-09-29 H. Christian Gromoll , Łukasz Kruk

We study a sequence of single server queues with customer abandonment (GI/GI/1+GI) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known ([20, 18]) that the…

Probability · Mathematics 2021-02-10 Chihoon Lee , Amy R. Ward , Heng-Qing Ye

We define a wide class of Markovian load balancing networks of identical single-server infinite-buffer queues. These networks may implement classic parallel server or work stealing load balancing policies, and may be asymmetric, for…

Networking and Internet Architecture · Computer Science 2024-07-08 Carl Graham

We present the first algorithm that samples $\max_{n\geq0}\{S_{n}-n^{\alpha}\},$ where $S_n$ is a mean zero random walk, and $n^{\alpha}$ with $\alpha\in(1/2,1)$ defines a nonliner boundary. We show that our algorithm has finite expected…

Probability · Mathematics 2016-09-27 Jose Blanchet , Jing Dong , Zhipeng Liu

We consider a system of $N$ parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any,…

Probability · Mathematics 2016-12-14 D. Mukherjee , S. C. Borst , J. S. H. van Leeuwaarden , P. A. Whiting

In this paper we models and studies a general vacation queueing model with impatient customers. We first propose a sufficient condition for the existence of the stationary workload process. We then give an integral equation for the…

Probability · Mathematics 2017-03-07 Assia Boumahdaf

A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…

Probability · Mathematics 2017-02-15 Sergey Foss , Alexander Stolyar

In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-03-23 Kuang Xu

Motivated by call center practice, we propose a tractable model for $\mbox{GI}/\mbox{GI}/n+\mbox{GI}$ queues in the efficiency-driven (ED) regime. We use a one-dimensional diffusion process to approximate the virtual waiting time process…

Probability · Mathematics 2015-09-17 Shuangchi He

We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows non-renewal external arrival…

Probability · Mathematics 2020-03-26 Ward Whitt , Wei You

This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate $\Lambda$ from a given distribution every $\Delta$…

Probability · Mathematics 2016-02-02 Mariska Heemskerk , Johan van Leeuwaarden , Michel Mandjes

Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…

Discrete Mathematics · Computer Science 2015-03-17 Ana Bušić , Bruno Gaujal , Furcy Pin

The discrete time queueing system is highly applicable to modern telecommunication systems, where it provides adaptive packet handling, congestion controlled security/inspection, energy efficient operation, and supports bursty traffic…

Information Theory · Computer Science 2026-02-27 Ashish Verma , Sourav Pradhan

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

In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a…

Probability · Mathematics 2008-08-01 Vyacheslav M. Abramov

This paper studies statistical inference in a network of infinite-server queues, with the aim of estimating the underlying parameters (routing matrix, arrival rates, parameters pertaining to the service times) using observations of the…

Probability · Mathematics 2025-06-10 Hritika Gupta , Michel Mandjes , Liron Ravner , Jiesen Wang

The problem of exact evaluation of the mean service cycle time in tandem systems of single-server queues with both infinite and finite buffers is considered. It is assumed that the interarrival and service times of customers form sequences…

Optimization and Control · Mathematics 2012-12-24 N. K. Krivulin , V. B. Nevzorov

We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…

Probability · Mathematics 2015-10-06 Junfei Huang , Hanqin Zhang , Jiheng Zhang

We study a generalization of the $M/G/1$ system (denoted by $rM/G/1$) with independent and identically distributed (iid) service times and with an arrival process whose arrival rate $\lambda_0f(r)$ depends on the remaining service time $r$…

Probability · Mathematics 2017-10-05 Benjamin Legros , Ali Devin Sezer

In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…

Machine Learning · Statistics 2025-05-07 Jung-hun Kim , Min-hwan Oh