English
Related papers

Related papers: On Sojourn Times in the Finite Capacity $M/M/1$ Qu…

200 papers

We consider a polling system where a group of an infinite number of servers visits sequentially a set of queues. When visited, each queue is attended for a random time. Arrivals at each queue follow a Poisson process, and service time of…

Probability · Mathematics 2014-04-23 Maria Vlasiou , Uri Yechiali

In this paper, we consider the M/GI/1 queue with single vacations under the gated service discipline. We obtain the probability generating function of the stationary queue length, the Laplace-Stieltjes transform of the system delay…

Probability · Mathematics 2026-04-14 Tetsuya Takine

We consider a processor sharing storage allocation model, which has m primary holding spaces and infinitely many secondary ones, and a single processor servicing the stored items (customers). All of the spaces are numbered and ordered. An…

Classical Analysis and ODEs · Mathematics 2009-07-22 Eunju Sohn , Charles Knessl

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

We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…

Probability · Mathematics 2018-08-23 Refael Hassin , Liron Ravner

We consider a cyclic polling system with general service times, general switch-over times, and simultaneous batch arrivals. This means that at an arrival epoch, a batch of customers may arrive simultaneously at the different queues of the…

Probability · Mathematics 2016-07-13 J. P. van der Gaast , M. B. M. de Koster , I. J. B. F. Adan

Tandem queues with finite buffer capacity commonly exist in practical applications. By viewing a tandem queue as an integrated system, an innovative approach has been developed to analyze its performance through the insight from reduction…

Performance · Computer Science 2016-06-02 Kan Wu , Ning Zhao

We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the…

Probability · Mathematics 2014-08-04 Marko Boon , Rob van der Mei , Erik Winands

In this article it is shown that if the busy period of a MGinf queue system is PME distributed, the service time is a random variable with a long tail distribution. The result is obtained through Laplace transforms analysis.

Probability · Mathematics 2021-10-18 Manuel Alberto M. Ferreira

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

In this paper we study the maximum queue length $M$ (in terms of the number of customers present) in a busy cycle in the M/G/1 queue. Assume that the service times have a logconvex density. For such (heavy-tailed) service-time distributions…

Probability · Mathematics 2007-05-23 Misja Nuyens

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

In this paper, we consider five models of heavy-tailed queues involving Mittag-Leffler distributions that generalize the classical $M/M/1$ queues. These models are suitable modifications of previously defined models in such a way that the…

Probability · Mathematics 2026-02-19 Giacomo Ascione , Luigia Caputo

The future Internet promises to support time-sensitive services that require ultra low latencies and reliabilities of 99.99%. Recent advances in cellular and WiFi connections enhance the network to meet high reliability and ultra low…

Networking and Internet Architecture · Computer Science 2022-12-26 Geraint I. Palmer , Jorge Martín-Pérez

Recent development of peer-to-peer (P2P) services (e.g. streaming, file sharing, and storage) systems introduces a new type of queue systems that receive little attention before, where both job and server arrive and depart randomly. Current…

Performance · Computer Science 2016-05-11 Taoyu Li , Minghua Chen , Tony Lee , Xing Li

We study the information-theoretic limit of reliable information processing by a server with queue-length dependent quality of service. We define the capacity for such a system as the number of bits reliably processed per unit time, and…

Information Theory · Computer Science 2016-03-08 Avhishek Chatterjee , Daewon Seo , Lav R. Varshney

We consider an M/M/Infinity service system in which an arriving customer is served by the first idle server in an infinite sequence S_1, S_2, ... of servers. We determine the first two terms in the asymptotic expansions of the moments of L…

Probability · Mathematics 2011-07-11 Patrick Eschenfeldt , Ben Gross , Nicholas Pippenger

We consider an $M/M/1$ queueing system with impatient customers with multiple and single vacations. It is assumed that customers are impatient whenever the state of the server. We derive the probability generating functions of the number of…

Probability · Mathematics 2016-04-12 Assia Boumahdaf

We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals…

Probability · Mathematics 2017-11-29 Onno Boxma , Sergey Foss , Jean-Marc Lasgouttes , Rudesindo Núñez Queija

We study the convergence of the $M/G/1$ processor-sharing, queue length process in the heavy traffic regime, in the finite variance case. To do so, we combine results pertaining to L\'{e}vy processes, branching processes and queuing theory.…

Probability · Mathematics 2013-12-04 Amaury Lambert , Florian Simatos , Bert Zwart