SINGLE SERVER QUEUES WITH A BATCH MARKOVIAN ARRIVAL PROCESS AND BULK RENEWAL OR NON-RENEWAL SERVICE

作     者：A.D.Banik 

作者机构：School of Basic SciencesIndian Institute of Technology 

出 版 物：《Journal of Systems Science and Systems Engineering》 (系统科学与系统工程学报（英文版）)

年 卷 期：2015年第24卷第3期

页      面：337-363页

核心收录：

学科分类：12[管理学] 02[经济学] 07[理学] 08[工学] 070103[理学-概率论与数理统计] 0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 0202[经济学-应用经济学] 020208[经济学-统计学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 0802[工学-机械工程] 0714[理学-统计学（可授理学、经济学学位）] 0811[工学-控制科学与工程] 0701[理学-数学] 081201[工学-计算机系统结构] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：partial financial support from the Department of Science and Technology New Delhi India under the research grant SR/FTP/MS-003/2012 

主　　题：Bulk service (a b)-rule system-length distribution infinite-buffer queue batch Markovian arrival process Markovian service process matrix-analytic procedure cost control cloud computing 

摘      要：We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum threshold size ＇a＇. The service time of each batch follows general distribution independent of each other as well as the arrival process. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Next we obtain queue-length distributions at various other epochs such as, pre-arrival, arbitrary and pre-service using relations with post-departure epoch. Later we also obtain the system-length distributions at post-departure and arbitrary epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue-lengths and mean waiting times have been obtained Total expected cost function per trait time is also derived to determine the locally optimal values of a and b. Secondly, we perform similar analysis for the corresponding infinite-buffer single server queue where arrivals occur according to a BMAP and service process in this case follows a non-renewal one, namely, Markovian service process （MSP）.