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In this paper, we study an $N$ server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as $N\to\infty$. This fluid limit depends on the initial number…

Probability · Mathematics 2021-08-24 Dennis Schol , Maria Vlasiou , Bert Zwart

We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this…

Performance · Computer Science 2021-05-25 Ravi Suman , Ananth Krishnamurthy

Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where…

Networking and Internet Architecture · Computer Science 2021-08-05 Muthukrishnan Senthil Kumar , Aresh Dadlani , Kiseon Kim

We consider a polling system with two queues, exhaustive service, no switch-over times and exponential service times. The waiting cost depends on the position of the queue relative to the server: It costs a customer c per time unit to wait…

Probability · Mathematics 2016-08-11 I. J. B. F. Adan , V. G. Kulkarni , N. Lee , A. A. J Lefeber

The $M/GI/m/n$ queueing system with $m$ homogeneous servers and the finite number $n$ of waiting spaces is studied. Let $\lambda$ be the customers arrival rate, and let $\mu$ be the reciprocal of the expected service time of a customer.…

Probability · Mathematics 2010-03-25 Vyacheslav M. Abramov

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 study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience…

Probability · Mathematics 2013-08-27 Jiheng Zhang

In this paper, we study the maximum waiting time $\max_{i\leq N}W_i(\cdot)$ in an $N$-server fork-join queue with heavy-tailed services as $N\to\infty$. The service times are the product of two random variables. One random variable has a…

Probability · Mathematics 2022-11-07 Dennis Schol , Maria Vlasiou , Bert Zwart

In this paper, we use a machine learning approach to predict the stationary distributions of the number of customers in a single-staiton multi server system. We consider two systems, the first is $c$ homogeneous servers, namely the…

Performance · Computer Science 2025-04-03 Eliran Sherzer

We give a simple derivation of the distribution of the maximum L of the length of the queue during a busy period for the M/M/1 queue with lambda<1 the ratio between arrival rate and service rate. We observe that the asymptotic behavior of…

Probability · Mathematics 2011-06-21 Patrick Eschenfeldt , Ben Gross , Nicholas Pippenger

In this paper, we deal with an $D/GI/1$ vacation system with impatient customers. We give a sufficient condition for the existence of a limit distribution of the waiting time and integral equations are derived in both reneging and balking…

Probability · Mathematics 2017-03-07 Assia Boumahdaf

A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent…

Probability · Mathematics 2025-02-21 Alexander Stolyar

We study a make-to-order system with a finite set of customers. Production is stochastic with a nonlinear dependence between the ordered quantity and the production rate. Customers may have to queue until their turn arrives, and therefore…

Optimization and Control · Mathematics 2025-07-29 Refael Hassin , Jiesen Wang

We consider a single server queue which has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level single server queue. This model is motivated by an energy saving problem for a…

Probability · Mathematics 2025-05-28 Masakiyo Miyazawa

In Naor's model [17], customers decide whether or not to join a queue after observing its length. This work considers a variation in which customers are heterogeneous in their service value (reward) $R$ from completed service and…

Statistics Theory · Mathematics 2026-03-25 Daniel Podorojnyi , Liron Ravner

This paper purpose is to investigate exponential behavior conditions for the infinite servers queue with Poisson arrivals busy period length distribution. It is presented a general theoretical result that is the basis of this work. The…

Probability · Mathematics 2021-09-30 Manuel Alberto M. Ferreira , José António Filipe

In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that…

Probability · Mathematics 2014-08-04 Marko Boon

We consider a set-up in which there are multiple servers and multiple clients in a large distributed computing system. Clients request servers to process jobs. Servers can only process one job in unit time. There is no coordinating agent to…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-10-18 Anindya S. Chakrabarti , Diptesh Ghosh

The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…

Probability · Mathematics 2021-09-23 Manuel Alberto M. Ferreira

We consider a system consisting of a server alternating between two service points. At both service points there is an infinite queue of customers that have to undergo a preparation phase before being served. We are interested in the…

Probability · Mathematics 2014-04-23 Maria Vlasiou , Ivo J. B. F. Adan