Product Form Solution of a Queuing-Inventory System with Lost Sales and Server Vacation  

作　　者：YUE Dequan ZHANG Yuying XU Xiuli YUE Wuyi 

机构地区：[1]School of Science,Yanshan University,Qinhuangdao 066004,China [2]School of Economics and Management,Yanshan University,Qinhuangdao 066004,China [3]The Kyoto College of Graduate Studies for Informatics,Kyoto City 606-8225,Japan

出　　处：《Journal of Systems Science & Complexity》2024年第2期729-758,共30页系统科学与复杂性学报（英文版）

基　　金：supported in part by the Natural Science Foundation of China under Grant No.71971189;the Natural Science Foundation of Hebei Province under Grant No.A2019203313;the Key Project of Scientific Research in Higher Education of Hebei Province of China under Grant No.ZD2018042;in part by MEXT,Japan。

摘　　要：In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time and the vacation time follow exponential distributions.The authors formulate the model as a quasi-birth-and-dearth(QBD)process and derive the stability condition of the system.Then,the stationary distribution in product form for the joint process of the queue length,the inventory level,and the server’s status is obtained.Furthermore,the conditional distributions of the inventory level when the server is on and operational,and when it is off due to a vacation,are derived.Using the stationary distribution,the authors obtain some performance measures of the system.The authors investigate analytically the effect of the server’s vacation on the performance measures.Finally,several numerical examples are presented to investigate the effects of some parameters on the performance measures,the optimal policy,and the optimal cost.

关 键 词：Cost function multiple vacations product form solution queuing-inventory system (s S)control policy 

分 类 号：O226[理学—运筹学与控制论] F274[理学—数学]