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Related papers: Poly-Exp Bounds in Tandem Queues

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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

For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system…

Probability · Mathematics 2017-02-06 Nikhil Bansal , Bart Kamphorst , Bert Zwart

We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation…

Probability · Mathematics 2013-02-14 Niek Bouman , Sem C. Borst , Onno J. Boxma , Johan S. H. van Leeuwaarden

Consider a system of $N$ parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. When a task arrives, the dispatcher assigns it to…

Probability · Mathematics 2019-01-25 Sayan Banerjee , Debankur Mukherjee

We introduce an extension of the M/M/1 queueing process with a spatial structure and excluded- volume effect. The rule of particle hopping is the same as for the totally asymmetric simple exclusion process (TASEP). A stationary-state…

Statistical Mechanics · Physics 2014-09-18 Chikashi Arita

We consider the FCFS $GI/GI/n$ queue in the Halfin-Whitt heavy traffic regime, and prove bounds for the steady-state probability of delay (s.s.p.d.) for generally distributed processing times. We prove that there exist $\epsilon_1,…

Probability · Mathematics 2016-09-02 David A. Goldberg

We study a G/GI/1 single-server queuing model with i.i.d.\ service times that are independent of a stationary process of inter-arrival times. We show that the distribution of the waiting time converges to a stationary law as time tends to…

Probability · Mathematics 2020-12-04 Attila Lovas , Miklós Rásonyi

We consider the problem of packet scheduling in single-hop queueing networks, and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric we use the delay stability of traffic flows: a…

Networking and Internet Architecture · Computer Science 2011-08-02 Mihalis G. Markakis , Eytan H. Modiano , John N. Tsitsiklis

Consider a countably infinite collection of interacting queues, with a queue located at each point of the $d$-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the…

Probability · Mathematics 2019-03-12 Abishek Sankararaman , François Baccelli , Sergey Foss

We consider a Generalised Jackson Network with finitely many servers, a renewal input and $i.i.d.$ service times at each queue. We assume the network to be stable and, in addition, the distribution of the inter-arrival times to have…

Probability · Mathematics 2025-07-01 Sergey Foss , Masakiyo Miyazawa , Linglong Yuan

This paper purpose is to investigate exponential behavior conditions for the infinite servers queue with Poisson arrivals busy period length distribution. It is presented a general theoretical result that is the basis of this work. The…

Probability · Mathematics 2021-09-30 Manuel Alberto M. Ferreira , José António Filipe

Consider an M/M/$s$ queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we…

When an explicit expression for a probability distribution function $F(x)$ can not be found, asymptotic properties of the tail probability function $\bar{F}(x)=1-F(x)$ are very valuable, since they provide approximations or bounds for…

Probability · Mathematics 2019-04-16 Bin Liu , Yiqiang Q. Zhao

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

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends…

Performance · Computer Science 2013-08-02 Florin Ciucu , Ramin Khalili , Yuming Jiang , Liu Yang , Yong Cui

The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket…

Statistical Mechanics · Physics 2015-02-02 C. Arita , A. Schadschneider

We consider a polling system: a queueing system of $N\ge 1$ queues with Poisson arrivals $Q_1,...,Q_N$ visited in a cyclic order (with or without switchover times) by a single server. For this system we derive the probability generating…

Probability · Mathematics 2011-11-09 Onno Boxma , Offer Kella , Kamil Marcin Kosinski

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

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

The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…

Probability · Mathematics 2021-09-23 Manuel Alberto M. Ferreira