Petri net analysis of a queueing inventory system with orbital search by the server
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), gene...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-05-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0207 |
| _version_ | 1797810870472933376 |
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| author | Ikhlef Lyes Hakmi Sedda Lekadir Ouiza Aïssani Djamil |
| author_facet | Ikhlef Lyes Hakmi Sedda Lekadir Ouiza Aïssani Djamil |
| author_sort | Ikhlef Lyes |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T07:15:19Z |
| format | Article |
| id | doaj.art-bbe54884c82a4f7f8dcc37c3e0f42eb6 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-03-13T07:15:19Z |
| publishDate | 2023-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-bbe54884c82a4f7f8dcc37c3e0f42eb62023-06-05T09:17:13ZengDe GruyterDemonstratio Mathematica2391-46612023-05-015612056206610.1515/dema-2022-0207Petri net analysis of a queueing inventory system with orbital search by the serverIkhlef Lyes0Hakmi Sedda1Lekadir Ouiza2Aïssani Djamil3Department of Mathematics, Faculty of Sciences, Research Unit LaMOS, University of Algiers, Algier, AlgeriaEconomic Sciences Faculty, Research Unit LaMOS, Bejaia University, Bejaia, AlgeriaOperation Research Department, Research Unit LaMOS, Exact Sciences Faculty, Bejaia University, Bejaia, AlgeriaOperation Research Department, Research Unit LaMOS, Exact Sciences Faculty, Bejaia University, Bejaia, AlgeriaIn 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.https://doi.org/10.1515/dema-2022-0207inventory modelsstochastic petri netsmarkov chainorbital search(s, s) policy60j27 |
| spellingShingle | Ikhlef Lyes Hakmi Sedda Lekadir Ouiza Aïssani Djamil Petri net analysis of a queueing inventory system with orbital search by the server Demonstratio Mathematica inventory models stochastic petri nets markov chain orbital search (s, s) policy 60j27 |
| title | Petri net analysis of a queueing inventory system with orbital search by the server |
| title_full | Petri net analysis of a queueing inventory system with orbital search by the server |
| title_fullStr | Petri net analysis of a queueing inventory system with orbital search by the server |
| title_full_unstemmed | Petri net analysis of a queueing inventory system with orbital search by the server |
| title_short | Petri net analysis of a queueing inventory system with orbital search by the server |
| title_sort | petri net analysis of a queueing inventory system with orbital search by the server |
| topic | inventory models stochastic petri nets markov chain orbital search (s, s) policy 60j27 |
| url | https://doi.org/10.1515/dema-2022-0207 |
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