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Related papers: On a Processor Sharing Queue That Models Balking

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Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times…

Probability · Mathematics 2017-01-13 Angelos Aveklouris , Maria Vlasiou , Jiheng Zhang , Bert Zwart

Motivated by demand prediction for the custodial prison population in England and Wales, this paper describes an approach to the study of service systems using infinite server queues, where the system has non-empty initial state and the…

Applications · Statistics 2023-02-23 Nikki Sonenberg , Victoria Volodina , Peter G. Challenor , Jim Q. Smith

This paper investigates the capacity of a channel in which information is conveyed by the timing of consecutive packets passing through a queue with independent and identically distributed service times. Such timing channels are commonly…

Information Theory · Computer Science 2018-03-06 Mehrnaz Tavan , Roy D. Yates , Waheed U. Bajwa

In this paper, we examine the Age of Information (AoI) of a source sending status updates to a monitor through a queue operating under the Processor Sharing (PS) discipline. In the PS queueing discipline, all the updates are served…

Information Theory · Computer Science 2023-09-06 Beñat Gandarias , Josu Doncel , Mohamad Assaad

In this paper we study the Markov-modulated M/M/$\infty$ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system's asymptotic behavior under a particular scaling of the…

Probability · Mathematics 2016-01-13 Joke Blom , Koen de Turck , Michel Mandjes

The Erlang A model--an M/M/s queue with exponential abandonment--is often used to represent a service system with impatient customers. For this system, the popular square-root staffing rule determines the necessary staffing level to achieve…

Probability · Mathematics 2021-12-07 Katsunobu Sasanuma , Robert Hampshire , Alan Scheller-Wolf

We consider a processor sharing queue where the number of jobs served at any time is limited to $K$, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this…

Probability · Mathematics 2012-07-02 Jiheng Zhang , J. G. Dai , Bert Zwart

We consider the problem of scheduling arrivals to a congestion system with a finite number of users having identical deterministic demand sizes. The congestion is of the processor sharing type in the sense that all users in the system at…

Optimization and Control · Mathematics 2017-04-12 Liron Ravner , Yoni Nazarathy

We consider a system of processor-sharing queues with state-dependent service rates. These are allocated according to balanced fairness within a polymatroid capacity set. Balanced fairness is known to be both insensitive and…

Performance · Computer Science 2019-10-25 Thomas Bonald , Céline Comte , Virag Shah , Gustavo de Veciana

We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the well-studied heavy…

Probability · Mathematics 2014-03-24 Rami Atar , Itai Gurvich

We consider a load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…

Probability · Mathematics 2023-04-05 Prakirt Raj Jhunjhunwala , Martin Zubeldia , Siva Theja Maguluri

We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…

Probability · Mathematics 2015-12-01 Gianmarco Bet , Remco van der Hofstad , Johan S. H. van Leeuwaarden

In this paper, we investigate the number of customers that overlap or coincide with a virtual customer in an Erlang-A queue. Our study provides a novel approach that exploits fluid and diffusion limits for the queue to approximate the mean…

Probability · Mathematics 2025-07-02 Young Myoung Ko , Jamol Pender , Jin Xu

This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…

Probability · Mathematics 2007-12-28 Guodong Pang , Rishi Talreja , Ward Whitt

In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a…

Probability · Mathematics 2015-11-13 Andrei Sleptchenko , Jori Selen , Ivo Adan , Geert-Jan van Houtum

In a superscalar processor, instructions of various types flow through an execution pipeline, traversing hardware resources which are mostly shared among many different instruction types. A notable exception to shared pipeline resources is…

Performance · Computer Science 2018-07-24 Shane Carroll , Wei-Ming Ling

In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a…

Probability · Mathematics 2008-08-01 Vyacheslav M. Abramov

We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is…

Probability · Mathematics 2007-11-06 Iain MacPhee , Mikhail Menshikov , Dimitri Petritis , Serguei Popov

In this paper we models and studies a general vacation queueing model with impatient customers. We first propose a sufficient condition for the existence of the stationary workload process. We then give an integral equation for the…

Probability · Mathematics 2017-03-07 Assia Boumahdaf

We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…

Probability · Mathematics 2017-08-21 Peter W. Glynn , Harsha Honnappa