• 论文 •

### 服务员多重休假的易逝品排队库存系统的稳态分析

1. 1. 燕山大学经济管理学院,秦皇岛 066004; 2. 燕山大学理学院,秦皇岛  066004
• 出版日期:2020-08-25 发布日期:2020-09-24

ZHANG Yuying, YUE Dequan. Steady State Analysis of a Perishable Queueing-Inventory System with Server's Multiple Vacation[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(8): 1473-1491.

### Steady State Analysis of a Perishable Queueing-Inventory System with Server's Multiple Vacation

ZHANG Yuying1 ,YUE Dequan2

1. 1. School of Economics and Management, Yanshan University, Qinhuangdao 066004; 2. School of Science, Yanshan University, Qinhuangdao 066004
• Online:2020-08-25 Published:2020-09-24

In this paper, we consider a continuous review $M/M/1$ queueing-inventory system with perishable items and $\left( {s,S}\right)$ policy, where the server takes multiple vacation which follows an exponential distribution when the on-hand inventory level is zero. Customers arrive according to a Poisson process, and the service time, the life time of each item and the lead time are assumed to be exponentially distributed. Firstly, the stability condition of the system is derived by using quasi-birth-and-death process theory. Then, we consider an $M/M/1$ inventory system with server's vacation where the service time is negligible. The steady-state distribution of the system is derived. Based on this distribution, we further analyze an $M/M/1$ queueing-inventory system with server's vacation and positive service time. The stationary joint distribution of the queue length, the on-hand inventory level and server status is obtained. Besides, some performance measures of the system and the expected cost function per unit time are calculated. Finally, the effect of the parameters on some important performance measures is analyzed by numerical examples. The optimal inventory policy and the optimal expected cost are calculated by using the genetic algorithm.

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 [1] 左凯, 吴文青, 张元元. 修理工多重休假且修理设备可更换的$n$中取$k$温贮备系统研究[J]. 系统科学与数学, 2021, 41(6): 1729-1741. [2] 贺灵悦，唐应辉. 带启动时间和多重休假的Min($N,V$)-策略$M/G/1$ 排队系统[J]. 系统科学与数学, 2017, 37(3): 846-862. [3] 孙玉玲,石岿然, 周晶. 考虑客户违约情况下的易逝品超售决策研究[J]. 系统科学与数学, 2011, 31(10): 1209-1217. [4] 杨乔礼;朱翼隽. 分布式多媒体系统媒体同步的排队模型分析[J]. 系统科学与数学, 2010, 30(Supplement): 593-603. [5] 杨乔礼;朱翼隽. 分布式多媒体系统媒体同步的排队模型分析[J]. 系统科学与数学, 2010, 30(5): 593-603. [6] 李成钢;田乃硕;赵冰;刘元慧. 多重休假的Bernoulli反馈M/G/1排队系统的稳态队长[J]. 系统科学与数学, 2009, 29(2): 162-167.