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

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0207

Lyes Ikhlef, Sedda Hakmi, Ouiza Lekadir, D. Aïssani

引用次数: 0

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.

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具有服务器轨道搜索的排队库存系统的Petri网分析

摘要本文研究了一个具有有限需求源、重试需求、服务时间、提前期、（s，s）\left（s，s）补货策略和从轨道上搜索需求的排队库存系统。当提前期是指数分布的（相应的提前期是一般分布的），针对该库存系统提出了广义随机Petri网（GSPN）（相应的马尔可夫再生随机Petri网[MRSPN]）。该随机Petri网模型的定量分析是由GSPN模型的连续时间马尔可夫链（MRSPN模型的补充变量法）获得的。获得了概率分布，这使我们能够计算所研究系统的性能指标和预期成本率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.