On transient queue-size distribution in the batch-arrivals system with a single vacation policy

Title:

On transient queue-size distribution in the batch-arrivals system with a single vacation policy

Creator:

Kempa, Woiciech M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1ca9fa79-31a4-4606-bb9a-1cb38f1e715a
uuid:1ca9fa79-31a4-4606-bb9a-1cb38f1e715a

Subject:

batch Poisson arrivals, queue-size distribution, renewal theory, single vacation, and transient state

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a "usual'' system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the analysis of the original system on a single vacation cycle is brought to the study of the "usual'' system. Finally, the renewal theory is used to derive the general result. Moreover, a numerical approach to analytical results is discussed and some illustrative numerical examples are given.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[126]-141

Source:

Kybernetika | 2014 Volume:50 | Number:1

Harvested from:

CDK

Metadata only:

false