Stationary Analysis and Optimal Control Under Multiple Working Vacation Policy in a GI/Ma,b/1 Queue

作     者：PANDA Gopinath BANIK Abhijit Datta GUHA Dibyajyoti 

作者机构：School of Mathematical Sciences National Institute of Science Education and Research Bhubaneswar-752050 India School of Basic Sciences Indian Institute of Technology Bhubaneswar-752050 India International Management Institute Kolkata-700027 India 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2018年第31卷第4期

页      面：1003-1023页

核心收录：

学科分类：0711[理学-系统科学] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：The authors would like to thank Dr. N K Jana  School of Mathematical Sciences  National Institute of Science Education and Research Bhubaneswar for his help to improve the language of presentation of the paper. We would also like to thank three anonymous referees for their insightful and constructive comments that helped us to upgrade the standard of the paper. Also  the authors would like to thank Dr. A K Ojha  School of Basic Sciences  Indian Institute of Technology Bhubaneswar for his thorough language editing before submitting the second revised version of this paper 

主　　题：Bulk service cost optimization mean idle period multiple working vacations roots method system-length 

摘      要：This paper considers an infinite buffer renewal input queue with multiple working vacation policy wherein customers are served by a single server according to general bulk service （a,b）-rule （1 ≤ a ≤ b）. If the number of waiting customers in the system at a service completion epoch （during a normal busy period） is lower than ＇a＇, then the server starts a vacation. During a vacation if the number of waiting customers reaches the minimum threshold size ＇a＇, then the server starts serving this batch with a lower rate than that of the normal busy period. After completion of a batch service during working vacation, if the server finds less than takes another vacation, otherwise the server rate. The maximum allowed size of a batch a＇ customers accumulated in the system, then the server continues to serve the available batch with that lower in service is ＇b＇. The authors derive both queue-length and system-length distributions at pre-arrival epoch using both embedded Markov chain approach and the roots method. The arbitrary epoch probabilities are obtained using the classical argument based on renewal theory. Several performance measures like average queue and system-length, mean waiting-time, cost and profit optimization are studied and numerically computed.