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Related papers: Losses in M/GI/m/n Queues

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Demand for studying queueing systems with multiple servers providing correlated services was created about 60 years ago, motivated by various applications. In recent years, the importance of such studies has been significantly increased,…

Probability · Mathematics 2026-04-16 Suman Thapa , Yiqiang Q. Zhao

In the present work we study Bayesian nonparametric inference for the continuous-time M/G/1 queueing system. In the focus of the study is the unobservable service time distribution. We assume that the only available data of the system are…

Statistics Theory · Mathematics 2017-09-22 Cornelia Wichelhaus , Moritz von Rohrscheidt

Single-server queues with customer abandonment arise in call centers and many service systems, but steady-state performance measures remain analytically intractable beyond Markovian assumptions. This paper develops Robust Queueing (RQ)…

Probability · Mathematics 2026-03-03 Wei You

A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the…

Probability · Mathematics 2011-08-05 Samantha Molinaro , Myron Hlynka , Shan Xu

Discrete-time queueing models find huge applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems, computer networks, etc. In this paper, we analyze an infinite-buffer queueing…

Probability · Mathematics 2023-01-13 U. C. Gupta , Nitin Kumar , S. Pradhan , F. P. Barbhuiya

In this paper, we consider discrete-time D-BMAP/G/\inf queueing model. We construct effective discrete-time Markovian dynamics for this model and utilize it to derive exact time-dependent distribution of customer number and the…

Probability · Mathematics 2025-05-30 Tonglin Liao , Youming Li

We analyze opportunistic schemes for transmission scheduling from one of $n$ homogeneous queues whose channel states fluctuate independently. Considered schemes consist of the LCQ policy, which transmits from a longest connected queue in…

Performance · Computer Science 2008-10-02 Murat Alanyali , Maxim Dashouk

In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…

Probability · Mathematics 2018-12-07 Abhishek , Rudesindo Núñez Queija , Marko Boon

The mathematics of the finite single server queue with Poisson input and semi-Markov service times($M/SM/1/b$) is similar to that used for $BMAP/G/1/b$ systems. This observation results in new analytical formulas for a queue size in the…

Probability · Mathematics 2018-06-15 Krzysztof Rusek , Zdzisław Papir

Queues with setup time are extensively studied because they have application in performance evaluation of power-saving data centers. In a data center, there are a huge number of servers which consume a large amount of energy. In the current…

Performance · Computer Science 2015-12-15 Tuan Phung-Duc

We study the MAP/M/s+G queuing model with MAP (Markovian Arrival Process) arrivals, exponentially distributed service times, infinite waiting room, and generally distributed patience times. Using sample-path arguments, we propose to obtain…

Performance · Computer Science 2021-10-22 Omer Gursoy , Kamal Adli Mehr , Nail Akar

The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon…

Probability · Mathematics 2021-07-01 Vyacheslav M. Abramov

The problems arising when the moments of service time distributions, for which the MGinf queue system busy period and busy cycle become very easy to study, are presented and it is shown how to overcome them. The busy cycle renewal function…

Probability · Mathematics 2021-10-08 Manuel Alberto M. Ferreira

We consider queueing models, where customers arrive according to a continuous-time binomial process on a finite interval. In this arrival process, a total of $K$ customers arrive in the finite time interval $[0,T]$, where arrival times of…

Probability · Mathematics 2024-12-10 Kaito Hayashi , Yoshiaki Inoue , Tetsuya Takine

In this paper, we consider the M/GI/1 queue with single vacations under the gated service discipline. We obtain the probability generating function of the stationary queue length, the Laplace-Stieltjes transform of the system delay…

Probability · Mathematics 2026-04-14 Tetsuya Takine

We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…

Probability · Mathematics 2014-12-09 Harsha Honnappa , Rahul Jain , Amy R. Ward

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 consider the so-called GI/GI/N queueing network in which a stream of jobs with independent and identically distributed service times arrive according to a renewal process to a common queue served by $N$ identical servers in a…

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

We introduce and study some queueing models with random resetting, including Markovian and non--Markovian models. The Markovian models include M/M/$\infty$, M/M/r and M/M/1+M queues with random resetting, in which a continuous-time Markov…

Probability · Mathematics 2025-11-27 Dongzhou Huang , Guodong Pang , Izabella Stuhl , Yuri Suhov

A result of Ward and Glynn (2005) asserts that the sequence of scaled offered waiting time processes of the $GI/GI/1+GI$ queue converges weakly to a reflected Ornstein-Uhlenbeck process (ROU) in the positive real line, as the traffic…

Probability · Mathematics 2019-08-23 Chihoon Lee , Amy R. Ward , Heng-Qing Ye