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A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic…

Computer Science and Game Theory · Computer Science 2021-12-21 Roberto Cominetti , José Correa , Neil Olver

We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also…

Probability · Mathematics 2024-07-12 Serguei Popov

We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is…

Probability · Mathematics 2008-03-19 David Gamarnik , Petar Momcilovic

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 studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite state Markov process that modulates the…

Probability · Mathematics 2012-11-30 Amarjit Budhiraja , Arka Ghosh , Xin Liu

We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may…

Performance · Computer Science 2015-03-18 U. Ayesta , M. Erausquin , M. Jonckheere , I. M. Verloop

Closed queuing networks with finite capacity buffers and skip-over policies are fundamental models in the performance evaluation of computer and communication systems. This technical report presents the details of computational algorithms…

Performance · Computer Science 2024-09-13 Gianfranco Balbo , Andrea Marin , Diletta Olliaro , Matteo Sereno

In this work we study the problem of asymptotically optimal control of a well-known multi-class queuing network, referred to as the ``crisscross network,'' in heavy traffic. We consider exponential inter-arrival and service times, linear…

Probability · Mathematics 2007-05-23 Amarjit Budhiraja , Arka Prasanna Ghosh

Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ with increments $(1,0)$, $(-1,0)$, $(0,1)$ and $(0,-1)$; $X$ represents, at arrivals and service completions, the lengths of two queues working in parallel whose service and…

Probability · Mathematics 2018-06-05 Kamil Demirberk Ünlü , Ali Devin Sezer

We address the problem of giving robust performance bounds based on the study of the asymptotic behavior of the insensitive load balancing schemes when the number of servers and the load scales jointly. These schemes have the desirable…

Performance · Computer Science 2016-05-11 Matthieu Jonckheere , Balakrishna Prabhu

We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…

Systems and Control · Electrical Eng. & Systems 2023-02-13 Adrien Banse , Zheming Wang , Raphaël M. Jungers

The Multi-class Queueing Network (McQN) arises as a natural multi-class extension of the traditional (single-class) Jackson network. In a single-class network subcriticality (i.e. subunitary nominal workload at every station) entails…

Probability · Mathematics 2018-12-17 Haralambie Leahu , Michel Mandjes , Ana-Maria Oprescu

A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…

Probability · Mathematics 2017-02-15 Sergey Foss , Alexander Stolyar

We study randomized experiments in a service system when stochastic congestion can arise from temporarily limited supply or excess demand. Such congestion gives rise to cross-unit interference between the waiting customers, and analytic…

Systems and Control · Electrical Eng. & Systems 2026-02-17 Shuangning Li , Ramesh Johari , Xu Kuang , Stefan Wager

In this paper we consider the problem of maximum throughput for tandem queueing system. We modeled this system as a Quasi-Birth-Death process. In order to do this we named level the number of customers waiting in the first buffer (including…

Performance · Computer Science 2015-12-21 Daniel Marian Merezeanu , Daniela Andone

Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set of boundary states and a structured…

Probability · Mathematics 2015-10-02 Jori Selen , Ivo J. B. F. Adan , Johan S. H. van Leeuwaarden

We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic…

Probability · Mathematics 2009-01-19 J. G. Dai , Wuqin Lin

One of the key performance measures in queueing systems is the exponential decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have…

Probability · Mathematics 2007-05-23 David Gamarnik , Sean Meyn

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized…

Probability · Mathematics 2007-05-23 Marc Lelarge

The tandem fluid queueing model is a useful tool for performance analysis and control design for a variety of transportation systems. In this article, we study the joint impact of stochastic capacity and spillback on the long-time…

Optimization and Control · Mathematics 2019-05-07 Li Jin , Saurabh Amin