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We study the asymptotic response time tail in the M/G/n multi-server queue with heavy-tailed (regularly varying) job sizes, a setting representative of modern computing workloads. For single-server systems, tail optimization is well…

Performance · Computer Science 2026-05-14 Zhouzi Li , Mor Harchol-Balter , Alan Scheller-Wolf

In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…

Statistics Theory · Mathematics 2013-05-27 Stanislav Volgushev , Xiaofeng Shao

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

We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\rho$ which is the ratio of mean service and mean…

Probability · Mathematics 2013-03-20 Sergey Foss , Dmitry Korshunov

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this…

Probability · Mathematics 2017-03-07 Mariska Heemskerk , Julia Kuhn , Michel Mandjes

This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow…

Statistics Theory · Mathematics 2019-06-25 Zeng Li , Fang Han , Jianfeng Yao

In this paper, we investigate overlap times in a two-dimensional infinite server tandem queue. Specifically, we analyze the amount of time that a pair of customers spend overlapping in any station of the two dimensional tandem network. We…

Probability · Mathematics 2024-03-13 Ruici Gao , Jamol Pender

We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals…

Probability · Mathematics 2017-11-29 Onno Boxma , Sergey Foss , Jean-Marc Lasgouttes , Rudesindo Núñez Queija

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

We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and…

Probability · Mathematics 2018-01-19 Abhishek , Marko Boon , Onno Boxma , Rudesindo Núñez-Queija

We consider the so-called GI/GI/N queue, in which a stream of jobs with independent and identically distributed service times arrive as a renewal process to a common queue that is served by $N$ identical parallel servers in a…

Probability · Mathematics 2017-12-06 Reza Aghajani , Kavita Ramanan

We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…

Optimization and Control · Mathematics 2025-05-29 Jonas Schießl , Ruchuan Ou , Timm Faulwasser , Michael Heinrich Baumann , Lars Grüne

We consider the $\Delta_{(i)}/G/1$ queue, in which a a total of $n$ customers independently demand service after an exponential time. We focus on the case of heavy-tailed service times, and assume that the tail of the service time…

Probability · Mathematics 2016-05-23 Gianmarco Bet , Remco van der Hofstad , Johan S. H. van Leeuwaarden

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

This paper considers a retrial queueing model for a base station in cellular networks where fresh calls and handover calls are available. Fresh calls are initiated from the cell of the base station. On the other hand, a handover call has…

Performance · Computer Science 2014-05-09 Kazuki Kajiwara , Tuan Phung-Duc

In this paper, we consider the state-dependent reflecting random walk on a half-strip. We provide explicit criteria for (positive) recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed…

Probability · Mathematics 2013-01-31 Wenming Hong , Meijuan Zhang , Yiqiang Q. Zhao

In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are…

Probability · Mathematics 2016-04-28 Mikael Petersson

In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…

Probability · Mathematics 2007-05-23 Eugene Ostrovsky

This paper proves a large deviation principle (LDP) for the stationary distribution of queue lengths in a subcritical generalised Jackson network assuming a Cramer condition on the interarrival and service times. The deviation function is…

Probability · Mathematics 2025-12-23 Anatolii A. Puhalskii

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