Displaying similar documents to “Busy period problems in the GI/G/∞ queue”

Joint distribution of the busy and idle periods of a discrete modified G I / G I / c / ∞ queue

Anatolij Dvurečenskij (1988)

Aplikace matematiky

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For a discrete modified G I / G I / c / ∞ queue, 1 ≤ c < ∞ , where the service times of all customers served during any busy period are independent random variables with not necessarily identical distribution functions, the joint distribution of the busy period, the subsequent idle period and the number of customers served during the busy period is derived. The formulae presented are in a convenient form for practical use. The paper is a continuation of [5], where the M / G I / c / ∞ discrete modified queue has been studied. ...

A discrete-time queueing system with changes in the vacation times

Ivan Atencia (2016)

International Journal of Applied Mathematics and Computer Science

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This paper considers a discrete-time queueing system in which an arriving customer can decide to follow a last come first served (LCFS) service discipline or to become a negative customer that eliminates the one at service, if any. After service completion, the server can opt for a vacation time or it can remain on duty. Changes in the vacation times as well as their associated distribution are thoroughly studied. An extensive analysis of the system is carried out and, using a probability...

On the Busy Period in One Finite Queue of M/G/1 Type with Inactive Orbit

Dragieva, Velika (2014)

Serdica Journal of Computing

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The paper deals with a single server finite queuing system where the customers, who failed to get service, are temporarily blocked in the orbit of inactive customers. This model and its variants have many applications, especially for optimization of the corresponding models with retrials. We analyze the system in non-stationary regime and, using the discrete transformations method study, the busy period length and the number of successful calls made during it. ACM Computing Classification...

A finite-buffer queue with a single vacation policy: an analytical study with evolutionary positioning

Marcin Woźniak, Wojciech M. Kempa, Marcin Gabryel, Robert K. Nowicki (2014)

International Journal of Applied Mathematics and Computer Science

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In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical...