Queueing Inventory System with Multiple Service Nodes and Addressed Retrials from a Common Orbit

IF 1 4区数学 Q3 STATISTICS & PROBABILITY Methodology and Computing in Applied Probability Pub Date : 2024-02-02 DOI:10.1007/s11009-023-10071-w

引用次数: 0

Abstract

In this paper, we consider a queueing inventory model with K service nodes located apart making it impossible to know the status of the other service nodes. The primary arrival of customers follows Marked Markovian Arrival Process and the service times are exponentially distributed. If a customer arriving at a node finds the server busy or the inventory level to be zero, he joins a common orbit with infinite capacity. An orbital customer shall choose a service node at random according to some predetermined probability distribution dependent on the orbit size. Each service node is assigned with a continuous review inventory replenished according to an (s, S) policy with lead time. This scenario is modeled as a level dependent quasi birth and death process which belongs to the class of asymptotically quasi-Teoplitz Markov chains. Steady-state probabilities and some important performance measures are obtained. A cost function is introduced and employed for computing the optimal values of reorder levels and replenishment rates.

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具有多个服务节点的队列盘存系统和从共同轨道出发的寻址重访系统

摘要本文考虑了一个排队库存模型，其中 K 个服务节点相距甚远，无法知道其他服务节点的状态。客户的主要到达遵循标记马尔可夫到达过程，服务时间呈指数分布。如果一个客户到达一个节点时发现服务器繁忙或库存水平为零，他就会加入一个具有无限容量的共同轨道。轨道客户应根据与轨道大小相关的某种预定概率分布随机选择一个服务节点。每个服务节点都会根据 (s, S) 政策被分配一个持续审查库存，并在有提前期的情况下进行补充。这种情况被模拟为一个依赖于水平的准出生和死亡过程，属于渐近的准特奥普利兹马尔可夫链。得出了稳态概率和一些重要的性能指标。引入了成本函数，并用于计算再订购水平和补货率的最优值。

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

Methodology and Computing in Applied Probability 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Methodology and Computing in Applied Probability will publish high quality research and review articles in the areas of applied probability that emphasize methodology and computing. Of special interest are articles in important areas of applications that include detailed case studies. Applied probability is a broad research area that is of interest to many scientists in diverse disciplines including: anthropology, biology, communication theory, economics, epidemiology, finance, linguistics, meteorology, operations research, psychology, quality control, reliability theory, sociology and statistics. The following alphabetical listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interests: -Algorithms- Approximations- Asymptotic Approximations & Expansions- Combinatorial & Geometric Probability- Communication Networks- Extreme Value Theory- Finance- Image Analysis- Inequalities- Information Theory- Mathematical Physics- Molecular Biology- Monte Carlo Methods- Order Statistics- Queuing Theory- Reliability Theory- Stochastic Processes