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In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and…

Probability · Mathematics 2009-02-27 Vijay G. Subramanian , Tara Javidi , Somsak Kittipiyakul

The discrete time queueing system is highly applicable to modern telecommunication systems, where it provides adaptive packet handling, congestion controlled security/inspection, energy efficient operation, and supports bursty traffic…

Information Theory · Computer Science 2026-02-27 Ashish Verma , Sourav Pradhan

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 discrete-time parallel service system consisting of $n$ heterogeneous single server queues with infinite capacity. Jobs arrive to the system as an i.i.d. process with rate proportional to $n$, and must be immediately…

Performance · Computer Science 2025-05-30 Yishun Luo , Martin Zubeldia

We prove that the scaled maximum steady-state waiting time and the scaled maximum steady-state queue length among $N$ $GI/GI/1$-queues in the $N$-server fork-join queue, converge to a normally distributed random variable as $N\to\infty$.…

Probability · Mathematics 2023-09-18 Dennis Schol , Maria Vlasiou , Bert Zwart

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 introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…

Physics and Society · Physics 2015-06-12 Misako Takayasu , Hayafumi Watanabe , Hideki Takayasu

In this note, we apply Stein's method to analyze the performance of general load balancing schemes in the many-server heavy-traffic regime. In particular, consider a load balancing system of $N$ servers and the distance of arrival rate to…

Probability · Mathematics 2020-04-28 Xingyu Zhou , Ness Shroff

We consider a system of N queues with decentralized load balancing such as power-of-D strategies(where D may depend on N) and generic scheduling disciplines. To measure the dependence of the queues, we use the clan of ancestors, a technique…

Probability · Mathematics 2018-09-17 Maria Clara Fittipaldi , Matthieu Jonckheere , Sergio I. Lopez

We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal.…

Probability · Mathematics 2007-05-23 Rami Atar , Avi Mandelbaum , Martin I. Reiman

This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers…

Probability · Mathematics 2007-05-23 Rami Atar

We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an infinitesimal time interval. We call it the Erlang queue…

Probability · Mathematics 2025-01-16 R. B. Pote , K. K. Kataria

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss networks. We use a variation of Dominated Coupling From The Past for which we simulate a…

Probability · Mathematics 2013-12-17 Jose Blanchet , Jing Dong

This paper studies many-server limits for multi-server queues that have a phase-type service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded $G/Ph/n+GI$ queues, where the…

Probability · Mathematics 2010-11-10 J. G. Dai , Shuangchi He , Tolga Tezcan

We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…

Probability · Mathematics 2017-01-02 Carlo Lancia , Gianluca Guadagni , Sokol Ndreca , Benedetto Scoppola

In classical asynchronous distributed systems composed of a fixed number n of processes where some proportion may fail by crashing, many objects do not have a wait-free linearizable implementation (e.g. stacks, queues, etc.). It has been…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-08-07 Grégoire Bonin , Achour Mostéfaoui , Matthieu Perrin

This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density $\lambda$ of the sets grows to infinity and the mean volume $\rho$ of the sets tends to zero. Assuming that the volume…

Probability · Mathematics 2011-11-10 Ingemar Kaj , Lasse Leskelä , Ilkka Norros , Volker Schmidt

We consider a sequence of single-server queueing models operating under a service policy that incorporates batches into processor sharing: arriving jobs build up behind a gate while waiting to begin service, while jobs in front of the gate…

Probability · Mathematics 2023-02-15 H. Christian Gromoll , Katelynn D. Kochalski

We study a many-server queuing system with general service time distribution and state dependent service rates. The dynamics of the system are modeled using measure valued processes which keep track of the residual service times. Under…

Probability · Mathematics 2013-04-09 Anup Biswas

We consider a finite population processor-sharing (PS) queue, with Markovian arrivals and an exponential server. Such a queue can model an interactive computer system consisting of a bank of terminals in series with a central processing…

Probability · Mathematics 2013-09-12 Qiang Zhen , Johan S. H. van Leeuwaarden , Charles Knessl