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We study positive recurrence and transience of a two-station network in which the behavior of the server in each station is governed by a Markov chain with a finite number of server states; this service process can represent various service…

Probability · Mathematics 2013-08-29 Toshihisa Ozawa

In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…

Performance · Computer Science 2019-04-12 Fabrice Guillemin , Veronica Quintuna Rodriguez

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

We investigate a processor sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue, or renege, before completing service. The corresponding stochastic processes are represented by…

Probability · Mathematics 2009-08-25 Christian H. Gromoll , Philippe Robert , Bert Zwart

Queueing systems with batch Markovian arrival process (BMAP) have paramount applications in the domain of wireless communication. The BMAP has been used to model the superposition of video sources and to approximate the super-position of…

Probability · Mathematics 2020-01-13 S. Pradhan , U. C. Gupta

In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a…

Probability · Mathematics 2017-05-02 Marko Boon , Onno Boxma , Offer Kella , Masakiyo Miyazawa

We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential…

Probability · Mathematics 2015-08-05 E. S. Badila , O. J. Boxma , J. A. C. Resing

In this paper we investigate an M/M/$\infty$ queue whose parameters depend on an external random environment that we assume to be a semi-Markovian process with finite state space. For this model we show a recursive formula that allows to…

Probability · Mathematics 2011-04-27 B. D'Auria

A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…

Probability · Mathematics 2012-04-30 Weining Kang , Kavita Ramanan

This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we…

Probability · Mathematics 2017-11-15 Dieter Fiems , Michel Mandjes , Brendan Patch

We introduce a queueing system that alternates between two modes, so-called {\it working mode} and {\it vacation mode}. During the working mode the system runs as an $M^{X}/G/1$ queue. Once the number of customers in the working mode drops…

Probability · Mathematics 2021-10-12 Igor Kleiner , Esther Frostig , David Perry

In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this…

Probability · Mathematics 2014-08-04 Marko Boon , Sandra van Wijk , Ivo Adan , Onno Boxma

We consider the $M/G/1$ queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution, in various asymptotic limits.…

Probability · Mathematics 2010-03-31 Qiang Zhen , Charles Knessl

We consider an infinite server queue where the arrival and the service rates are both modulated by a stochastic environment governed by an $S$-valued stochastic process $X$ that is ergodic with a limiting measure $\pi\in \mathcal{P}(S)$.…

Probability · Mathematics 2024-10-30 Abhishek Pal Majumder

We analyze an M/M/1 queue with a service discipline in which customers, upon arriving when the server is busy, search a sequence of stations for a vacant station at which to wait, and in which the server, upon becoming free when one or more…

Probability · Mathematics 2011-08-29 Patrick Eschenfeldt , Ben Gross , Nicholas Pippenger

This paper concerns the recurrence structure of the infinite server queue, as viewed through the prism of the maximum dater sequence, namely the time to drain the current work in the system as seen at arrival epochs. Despite the importance…

Probability · Mathematics 2026-01-12 Sergey Foss , Peter Glynn

This paper studies the diffusion limit for a network of infinite-server queues operating under Markov modulation (meaning that the system's parameters depend on an autonomously evolving background process). In previous papers on (primarily…

Probability · Mathematics 2017-12-13 H. M. Jansen , M. Mandjes , K. De Turck , S. Wittevrongel

In this paper, we study Markov-dependent reflected autoregressive processes, and other related models the analysis of which results in a vector-valued fixed-point functional equation of a certain type. In queueing terms, such processes…

Probability · Mathematics 2025-06-23 Ioannis Dimitriou

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in…

Probability · Mathematics 2020-01-01 Michel Mandjes , Nicos Starreveld , René Bekker