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Related papers: Batch sojourn time in polling systems on a circle

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We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the…

Probability · Mathematics 2014-08-04 Marko Boon , Rob van der Mei , Erik Winands

In this paper, we deal with a two-queue polling system attended by a single server. The server visits the queues according to a Markovian routing mechnism. There are two-class customers in the first queue. Customers of each queue are served…

Probability · Mathematics 2014-11-04 Yuqing Chu , Zaiming Liu , Jinbiao Wu

We consider gated polling systems with two special features: (i) retrials, and (ii) glue or reservation periods. When a type-$i$ customer arrives, or retries, during a glue period of station $i$, it will be served in the next visit period…

Probability · Mathematics 2016-10-20 Murtuza Ali Abidini , Onno Boxma , Bara Kim , Jeongsim Kim , Jacques Resing

In this paper, we analyze the sojourn of an entire batch in a processor sharing $M^{[X]}/M/1$ processor queue, where geometrically distributed batches arrive according to a Poisson process and jobs require exponential service times. By…

Probability · Mathematics 2020-09-29 Fabrice Guillemin , Alain Simonian , Ridha Nasri , Veronica Quintuna Rodriguez

We consider a single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer's sojourn time in two regimes: the customer…

Probability · Mathematics 2018-08-01 Sergey Foss , Masakiyo Miyazawa

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

We consider the $M/M/1$-PS queue with processor sharing. We study the conditional sojourn time distribution of an arriving customer, conditioned on the number of other customers present. A new formula is obtained for the conditional sojourn…

Probability · Mathematics 2010-03-16 Qiang Zhen , Charles Knessl

This article deals with asynchronous server vacation and customer retrial facility in a multi-server queueing-inventory system. The Poisson process governs the arrival of a customer. The system is comprised of c identical servers, a…

Optimization and Control · Mathematics 2023-07-31 K. Jeganathan , T. Harikrishnan , K. Prasanna Lakshmi , D. Nagarajan

We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is…

Probability · Mathematics 2007-11-06 Iain MacPhee , Mikhail Menshikov , Dimitri Petritis , Serguei Popov

We present an example of a single-server polling system with two queues and an adaptive service policy where the stability region depends on the expected values of all the primitives and also on a certain exponential moment of the…

Probability · Mathematics 2014-10-09 Natalia Chernova , Sergey Foss , Bara Kim

We consider large fluctuations, namely overload of servers, in a network with dynamic routing of messages. The servers form a circle. The number of input flows is equal to the number of servers, the messages of any flow are distributed…

Probability · Mathematics 2008-03-19 E. A. Pechersky , N. D. Vvedenskaya

A single server retrial queueing system with two-classes of orbiting customers, and general class dependent service times is considered. If an arriving customer finds the server unavailable, it enters a virtual queue, called the orbit,…

Probability · Mathematics 2018-02-22 Ioannis Dimitriou

In this paper we consider a single-server polling system with switch-over times. We introduce a new service discipline, mixed gated/exhaustive service, that can be used for queues with two types of customers: high and low priority…

Probability · Mathematics 2014-08-04 Marko Boon , Ivo Adan

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

We consider a polling system: a queueing system of $N\ge 1$ queues with Poisson arrivals $Q_1,...,Q_N$ visited in a cyclic order (with or without switchover times) by a single server. For this system we derive the probability generating…

Probability · Mathematics 2011-11-09 Onno Boxma , Offer Kella , Kamil Marcin Kosinski

We analyze the latency or sojourn time L(m,n) for the last customer in a batch of n customers to exit from the m-th queue in a tandem of m queues in the setting where the queues are in equilibrium before the batch of customers arrives at…

Probability · Mathematics 2014-04-21 Jinho Baik , Raj Rao Nadakuditi

The interest to retrial queueing systems is due to their application to telephone systems. The paper studies multiserver retrial queueing systems with $n$ servers. Arrival process is a quite general point process. An arriving customer…

Probability · Mathematics 2021-06-30 Vyacheslav M. Abramov

We consider a finite population processor-sharing (PS) queue, with Markovian arrivals and an exponential server. Such a queue can model an interactive computer system consisting of a bank of terminals in series with a central processing…

Probability · Mathematics 2013-09-12 Qiang Zhen , Johan S. H. van Leeuwaarden , Charles Knessl

A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…

Probability · Mathematics 2017-02-15 Sergey Foss , Alexander Stolyar

We consider sojourn or response times in processor-shared queues that have a finite population of potential users. Computing the response time of a tagged customer involves solving a finite system of linear ODEs. Writing the system in…

Probability · Mathematics 2013-09-12 Qiang Zhen , Charles Knessl