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Related papers: Finite-pool queues with heavy-tailed services

200 papers

A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routing choices) form a tree (in…

Probability · Mathematics 2014-03-28 Alexander Stolyar

We simulate queues of activity in a directed sandpile automaton in 1+1 dimensions by adding grains at the top row with driving rate $0 < r \leq 1$. The duration of elementary avalanches is exactly described by the distribution $P_1(t) \sim…

Statistical Mechanics · Physics 2009-10-31 Bosiljka Tadic , Vyatcheslav Priezzhev

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the…

Statistical Mechanics · Physics 2011-12-30 S. I. Denisov , S. B. Yuste , Yu. S. Bystrik , H. Kantz , K. Lindenberg

The model is a "generalized switch", serving multiple traffic flows in discrete time. The switch uses MaxWeight algorithm to make a service decision (scheduling choice) at each time step, which determines the probability distribution of the…

Probability · Mathematics 2015-02-13 Rahul Singh , Alexander Stolyar

In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service…

Probability · Mathematics 2017-07-14 Mayank Saxena , Onno Boxma , Stella Kapodistria , Rudesindo Núñez Queija

In this paper we consider a single-server cyclic polling system. Between visits to successive queues, the server is delayed by a random switch-over time. The order in which customers are served in each queue is determined by a priority…

Probability · Mathematics 2014-08-05 Marko Boon , Ivo Adan , Onno Boxma

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

Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of…

Probability · Mathematics 2014-05-02 Eleni Vatamidou , Ivo J. B. F. Adan , Maria Vlasiou , Bert Zwart

We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. In this work we are…

Probability · Mathematics 2023-11-07 Sayan Banerjee , Amarjit Budhiraja , Amber L. Puha

We consider a two-node tandem queueing network in which the upstream queue is GI/GI/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. To…

Probability · Mathematics 2018-10-01 H. Christian Gromoll , Bryce Terwilliger , Bert Zwart

We carry out a delay stability analysis (i.e., determine conditions under which expected steady-state delays at a queue are finite) for a simple 3-queue system operated under the Max-Weight scheduling policy, for the case where one of the…

Systems and Control · Computer Science 2012-07-25 Mihalis G. Markakis , Eytan Modiano , John N. Tsitsiklis

A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…

Probability · Mathematics 2012-04-30 Weining Kang , Kavita Ramanan

We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate…

Probability · Mathematics 2017-02-08 H. Christian Gromoll , Bryce Terwilliger , Bert Zwart

In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is delayed by a random switch-over time. Two types of customers arrive at the first queue: high and…

Probability · Mathematics 2014-08-04 Marko Boon , Ivo Adan , Onno Boxma

In this paper, we investigate overlap times in a two-dimensional infinite server tandem queue. Specifically, we analyze the amount of time that a pair of customers spend overlapping in any station of the two dimensional tandem network. We…

Probability · Mathematics 2024-03-13 Ruici Gao , Jamol Pender

In the literature, retrial queues with batch arrivals and heavy service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The…

Probability · Mathematics 2020-08-13 Bin Liu , Jie Min , Yiqiang Q. Zhao

Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length distribution, which is not addressed in [1]. In this paper,…

Probability · Mathematics 2026-04-13 Masahiro Kobayashi , Masakiyo Miyazawa , Yutaka Sakuma

We consider $M/G/\infty$ queues with gated service and obtain results on the distribution of the stage length and the number of customers served in a stage when the system is stationary. The stage length density is expressed as an infinite…

Probability · Mathematics 2026-03-23 Dimitra Pinotsi , Michael A. Zazanis

We prove a heavy traffic scaling limit for a shortest remaining processing time queue. We are interested in the case where the processing time distribution has a tail that decays rapidly, i.e., has light tails. In particular, we revisit the…

Probability · Mathematics 2023-11-07 Chunxu Ji , Amber L. Puha

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