Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Stankevich E. P., Tananko I. E., Dolgov V. I. Analysis of Closed Queueing Networks with Batch Service. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 4, pp. 527-533. DOI: 10.18500/1816-9791-2020-20-4-527-533, EDN: CCNNQT

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2020
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English
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Article
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519.872
EDN: 
CCNNQT

Analysis of Closed Queueing Networks with Batch Service

Autors: 
Stankevich Elena Petrovna, Saratov State University
Tananko Igor' Evstaf'evich, Saratov State University
Dolgov Vitalii Igorevich, Saratov State University
Abstract: 

We consider a closed queuing network with batch service and movements of customers in continuous time. Each node in the queueing network is an infinite capacity single server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. Customers are served in batches of a fixed size. If a number of customers in a node is less than the size, the server of the system is idle until the required number of customers arrive at the node. An arriving at a node customer is placed in the queue if the server is busy. The batсh service time is exponentially distributed. After a batсh finishes its execution at a node, each customer of the batch, regardless of other customers of the batch, immediately moves to another node in accordance with the routing probability. This article presents an analysis of the queueing network using a Markov chain with continuous time. The qenerator matrix is constructed for the underlying Markov chain. We obtain expressions for the performance measures. Some numerical examples are provided. The results can be used for the performance analysis manufacturing systems, passenger and freight transport systems, as well as information and computing systems with parallel processing and transmission of information.

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Received: 
15.06.2019
Accepted: 
23.07.2020
Published: 
30.11.2020