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Related papers: On mean-field \(GI/GI/1\) queueing model: existenc…

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The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain without jumps from level "infinity" to level zero. For simplicity,…

Probability · Mathematics 2014-06-30 Hiroyuki Masuyama

Explicit and exact results are obtained for the joint queue-length distribution for the two-level non-preemptive Markovian priority queue. Marginal distributions are derived for the general multi-level problem. The results are based on a…

Probability · Mathematics 2023-12-08 Josef Zuk , David Kirszenblat

A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…

Probability · Mathematics 2020-01-10 Yana Belopolskaya , Guodong Pang , Andrey Sarantsev , Yurii Suhov

Explicit results are obtained using simple and exact methods for the joint queue-length distribution of the M/M/c queue with an arbitrary number of non-preemptive priority levels. This work is the first to provide explicit results for the…

Probability · Mathematics 2023-11-06 Josef Zuk , David Kirszenblat

In this paper, we prove a characterization theorem on the number of losses during a busy period in $GI^X/GI^Y/1/n$ queueing systems, in which interarrival time distribution belongs to the class NWUE.

Probability · Mathematics 2013-01-16 Vyacheslav M. Abramov

A single queueing system with time-dependent exponentially distributed arrival processes and exponential machine processes (Kendall notation $M_t/M_t/1$) is analyzed. Modeling the time evolution for the discrete queue-length distribution by…

Probability · Mathematics 2018-12-21 Dieter Armbruster , Simone Göttlich , Stephan Knapp

This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The…

Probability · Mathematics 2013-03-28 Richard G. Clegg

The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…

Probability · Mathematics 2015-10-20 Y. Belopolskaya , Y. Suhov

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

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…

Probability · Mathematics 2018-12-05 F. Baccelli , A. Rybko , S. Shlosman , A. Vladimirov

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

We consider a Markovian single server queue in which customers are preemptively scheduled by exogenously assigned priority levels. The novelty in our model is that the priority levels are randomly assigned from a continuous probability…

Probability · Mathematics 2017-01-09 Neal Master , Zhengyuan Zhou , Nicholas Bambos

We consider the queuing networks, which are made from servers, exchanging their positions. The customers, using the network, try to reach their destinations, which is complicated by the movements of the servers, taking their customers with…

Probability · Mathematics 2013-11-18 François Baccelli , Alexandre Rybko , Senya Shlosman

The problem of reservation in a large distributed system is analyzed via a new mathematical model. A typical application is a station-based car-sharing system which can be described as a closed stochastic network where the nodes are the…

Probability · Mathematics 2024-10-01 Christine Fricker , Hanene Mohamed

The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…

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

Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…

Probability · Mathematics 2016-03-01 Benjamin Armbruster

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

The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…

Probability · Mathematics 2009-12-15 Carl Graham , Philippe Robert

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

Quantum computing is revolutionizing various fields, including operations research and queueing theory. This study presents a quantum method for simulating single-server Markovian (M/M/1) queues, making quantum computing more accessible to…

Quantum Physics · Physics 2024-10-14 Michal Koren , Or Peretz