Petri net analysis of a queueing inventory system with orbital search by the server-Reference-Cited by-同舟云学术

Petri net analysis of a queueing inventory system with orbital search by the server

Published:2023-01-01 Issue:1 Volume:56 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Ikhlef Lyes¹,Hakmi Sedda²,Lekadir Ouiza³,Aïssani Djamil³

Affiliation:

1. Department of Mathematics, Faculty of Sciences, Research Unit LaMOS, University of Algiers , Algier , Algeria

2. Economic Sciences Faculty, Research Unit LaMOS, Bejaia University , Bejaia , Algeria

3. Operation Research Department, Research Unit LaMOS, Exact Sciences Faculty, Bejaia University , Bejaia , Algeria

Abstract

Abstract In this article, a queueing inventory system with finite sources of demands, retrial demands, service time, lead time,

( s , S )

\left(s,S)

replenishment policy, and demands search from the orbit was studied. When the lead time is exponentially distributed (resp. lead time is generally distributed), generalized stochastic Petri net (GSPN) (resp. Markov regenerative stochastic Petri net [MRSPN]) is proposed for this inventory system. The quantitative analysis of this stochastic Petri net model was obtained by continuous time Markov chain for the GSPN model (resp. the supplementary variable method for the MRSPN model). The probability distributions are obtained, witch allowed us to compute performance measures and the expected cost rate of the studied system.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0207/pdf

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