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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

We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this…

Performance · Computer Science 2021-05-25 Ravi Suman , Ananth Krishnamurthy

In this paper we study the large deviations of time averaged mean square displacement (TAMSD) for Gaussian processes. The theory of large deviations is related to the exponential decay of probabilities of large fluctuations in random…

Probability · Mathematics 2018-11-29 J. Gajda , A. Wylomanska , H. Kantz , A. V. Chechkin , G. Sikora

In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of L\'evy input, covering compound Poisson, $\alpha$-stable L\'evy motion (with $1<\alpha<2$), and Brownian…

Probability · Mathematics 2017-03-14 David T. Koops , Onno J. Boxma , Michel R. H. Mandjes

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

Probability · Mathematics 2014-09-11 Marko Boon , Rob van der Mei , Erik Winands

Consider a queueing system fed by traffic from $N$ independent and identically distributed marked point processes. We establish several novel sample path large deviations results in the scaled uniform topology for such a system with a small…

Probability · Mathematics 2019-12-11 James R. Cruise , Fraser Daly , Bemsibom Toh

Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…

Methodology · Statistics 2019-06-28 Iker Perez , Giuliano Casale

Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the…

Probability · Mathematics 2018-01-19 Nigel Bean , Giang T. Nguyen , Federico Poloni

This paper is devoted to the problem of sample path large deviations for the Markov processes on R_+^N having a constant but different transition mechanism on each boundary set {x:x_i=0 for i\notin\Lambda, x_i>0 for i\in\Lambda}. The global…

Probability · Mathematics 2007-05-23 Irina Ignatiouk-Robert

We study a simple rate control scheme for a multiclass queuing network for which customers are partitioned into distinct flows that are queued separately at each station. The control scheme discards customers that arrive to the network…

Probability · Mathematics 2013-07-16 John Musacchio , Jean Walrand

We consider a system with N unit-service-rate queues in tandem, with exogenous arrivals of rate lambda at queue 1, under a back-pressure (MaxWeight) algorithm: service at queue n is blocked unless its queue length is greater than that of…

Probability · Mathematics 2010-02-23 Alexander Stolyar

In this paper, we consider an $N$-queue overloaded polling network attended by a single cyclically roving server. Upon the completion of his service, a customer is either routed to another queue or leaves the system. All the switches are…

Probability · Mathematics 2017-01-17 Zaiming Liu , Yuejiao Wang , Yuqing Chu , Yingqiu Li

In general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we establish bounds for the tail probabilities of queue lengths. Specifically, we examine queueing systems under Heavy-Traffic (HT)…

Probability · Mathematics 2023-06-21 Prakirt Raj Jhunjhunwala , Daniela Hurtado-Lange , Siva Theja Maguluri

In this paper, we analyze a shared access network with a fixed primary node and randomly distributed secondary nodes whose distribution follows a Poisson point process (PPP). The secondaries use a random access protocol allowing them to…

Networking and Internet Architecture · Computer Science 2016-03-30 Zheng Chen , Nikolaos Pappas , Marios Kountouris , Vangelis Angelakis

In this paper, we deal with a two-queue polling system attended by a single server. The server visits the queues according to a Markovian routing mechnism. There are two-class customers in the first queue. Customers of each queue are served…

Probability · Mathematics 2014-11-04 Yuqing Chu , Zaiming Liu , Jinbiao Wu

Gaitonde and Tardos recently studied a model of queueing networks where queues compete for servers and re-send returned packets in future rounds. They quantify the amount of additional processing power that guarantees a decentralized…

Computer Science and Game Theory · Computer Science 2022-10-18 Hu Fu , Qun Hu , Jia'nan Lin

In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the joint queue length process. Under passage…

Probability · Mathematics 2014-10-24 Maria Frolkova , Sergey Foss , Bert Zwart

Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…

Computation · Statistics 2017-11-02 Iker Perez , David Hodge , Theodore Kypraios

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The…

Probability · Mathematics 2009-09-29 Paul Dupuis , Ali Devin Sezer , Hui Wang

In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service…

Probability · Mathematics 2015-08-28 Wanyang Dai