batch arrivals in a compound Poisson process;
general (arbitrary) service;
optional re-service;
steady state queue size distribution;
average queue size;
average waiting time;
D O I:
10.1016/j.amc.2003.11.037
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
We study a single server queue with batch arrivals and general (arbitrary) service time distribution. The server provides service to customers, one by one, on a first come, first served basis. Just after completion of his service, a customer may leave the system or may opt to repeat his service, in which case this customer rejoins the queue. Further, just after completion of a customer's service the server may take a vacation of random length or may opt to continue staying in the system to serve the next customer. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average number of customers and the average waiting time in the queue. Some special cases of interest are discussed and some known results have been derived. A numerical illustration is provided. (C) 2004 Elsevier Inc. All rights reserved.
机构:
Sichuan Univ Sci & Engn, Sch Math & Stat, Zigong 643000, Sichuan, Peoples R ChinaSichuan Univ Sci & Engn, Sch Math & Stat, Zigong 643000, Sichuan, Peoples R China
Lan, Shaojun
Tang, Yinghui
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h-index: 0|
机构:
Sichuan Normal Univ, Sch Fundamental Educ, Chengdu 610068, Sichuan, Peoples R ChinaSichuan Univ Sci & Engn, Sch Math & Stat, Zigong 643000, Sichuan, Peoples R China
机构:
UNIV ELECT SCI & TECHNOL CHINA,DEPT MATH APPL,CHENGDU 610054,PEOPLES R CHINAUNIV ELECT SCI & TECHNOL CHINA,DEPT MATH APPL,CHENGDU 610054,PEOPLES R CHINA
机构:
Sichuan Normal Univ, Sch Math & Software Sci, Chengdu 610066, Peoples R ChinaSichuan Normal Univ, Sch Math & Software Sci, Chengdu 610066, Peoples R China