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Related papers: Heavy Traffic Limit for a Tandem Queue with Identi…

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We provide upper bounds on the end-to-end backlog and delay in a network with heavy-tailed and self-similar traffic. The analysis follows a network calculus approach where traffic is characterized by envelope functions and service is…

Networking and Internet Architecture · Computer Science 2013-12-30 Jorg Liebeherr , Almut Burchard , Florin Ciucu

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

Speed scaling for a tandem server setting is considered, where there is a series of servers, and each job has to be processed by each of the servers in sequence. Servers have a variable speed, their power consumption being a convex…

Data Structures and Algorithms · Computer Science 2019-07-11 Rahul Vaze , Jayakrishnan Nair

This paper studies the heavy-traffic joint distribution of queue lengths in two stochastic processing networks (SPN), viz., an input-queued switch operating under the MaxWeight scheduling policy and a two-server parallel server system…

Probability · Mathematics 2023-09-19 Prakirt Raj Jhunjhunwala , Siva Theja Maguluri

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

This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide…

Probability · Mathematics 2024-09-05 B. R. Vinay Kumar , Lasse Leskelä

In this paper we present the fluid limit of an heavily loaded Earliest Deadline First queue with impatient customers, represented by a measure-valued process keeping track of residual time-credits of lost and waiting customers. This fluid…

Probability · Mathematics 2007-05-23 Laurent Decreusefond , Pascal Moyal

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

We consider a Markovian single server queue with impatient customers. There is a customer abandonment cost and a holding cost for customers in the system. We consider two versions of the problem. In the first version, customers pay a reward…

Optimization and Control · Mathematics 2025-11-12 Runhua Wu , Hayriye Ayhan

Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…

Probability · Mathematics 2017-10-13 Reza Aghajani , Kavita Ramanan

We consider a multi-server queueing system under the power-of-two policy with Poisson job arrivals, heterogeneous servers and a general job requirement distribution; each server operates under the first-come first-serve policy and there are…

Performance · Computer Science 2017-01-24 Ane Izagirre , Armand M. Makowski

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

The mathematics of the finite single server queue with Poisson input and semi-Markov service times($M/SM/1/b$) is similar to that used for $BMAP/G/1/b$ systems. This observation results in new analytical formulas for a queue size in the…

Probability · Mathematics 2018-06-15 Krzysztof Rusek , Zdzisław Papir

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

We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions…

Probability · Mathematics 2019-03-19 Asaf Cohen

Motivated by emerging applications in online matching platforms and marketplaces, we study a matching queue. Customers and servers that arrive in a matching queue depart as soon as they are matched. While state-dependent control is an…

Probability · Mathematics 2024-12-03 Sushil Mahavir Varma , Siva Theja Maguluri

We consider the fundamental problem of managing a bounded size queue buffer where traffic consists of packets of varying size, where each packet requires several rounds of processing before it can be transmitted from the queue buffer. The…

Networking and Internet Architecture · Computer Science 2013-09-06 Kirill Kogan , Alejandro Lopez-Ortiz , Sergey I. Nikolenko , Gabriel Scalosub , Michael Segal

We study a queueing network with a strictly upper-triangular routing matrix, where each column contains at most one non-negative entry, and the root node receives input from a spectrally positive L\'{e}vy process. Our aim is to characterize…

Probability · Mathematics 2026-02-05 Krzysztof Dȩbicki , Nikolai Kriukov , Michel Mandjes

We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy…

Probability · Mathematics 2012-10-04 H. Christian Gromoll , Łukasz Kruk , Amber L. Puha

We study tandem queueing systems in which servers work more efficiently in teams than on their own and customers are impatient in that they may leave the system while waiting for service. Our goal is to determine the server assignment…

Probability · Mathematics 2026-01-23 Bihan Chatterjee , Sigrún Andradóttir , Hayriye Ayhan