The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations

被引：3
作者：
Cheng, Jiang [1 ,2 ]
Tang, Yinghui [1 ]
Yu, Miaomiao [1 ,3 ]
机构：
[1] Sichuan Normal Univ, Sch Math & Software Sci, Chengdu 610066, Sichuan, Peoples R China
[2] Southwest Univ Nationalities, Coll Comp Sci & Technol, Chengdu 610041, Sichuan, Peoples R China
[3] Sichuan Univ Sci & Engn, Sch Sci, Zigong 643000, Sichuan, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS | 2013年
基金：
中国国家自然科学基金;
关键词：
GI/GEO/1; QUEUE;
D O I：
10.1155/2013/587269
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with a discrete-time bulk-service Geo/Geo/1 queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at time n. The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer's observation epoch are investigated. Numerical experiment is performed to validate the analytical results.
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页数：10
相关论文
共 26 条
[1]   Algorithmic analysis of the discrete time GIX/GY/1 queueing system [J].
Alfa, Attahiru S. ;
He, Qi-Ming .
PERFORMANCE EVALUATION, 2008, 65 (09) :623-640
[2]  
[Anonymous], 1971, Schaum's outline of: Theory and Problems of Calculus of Finite Differences and Difference Equations
[3]   Analysis of a GI/M/1 queue with multiple working vacations [J].
Baba, Y .
OPERATIONS RESEARCH LETTERS, 2005, 33 (02) :201-209
[4]  
Banerjee A., 2011, International Journal of Operational Research, V12, P294, DOI 10.1504/IJOR.2011.042918
[5]   Reducing congestion in bulk-service finite-buffer queueing system using batch-size-dependent service [J].
Banerjee, A. ;
Gupta, U. C. .
PERFORMANCE EVALUATION, 2012, 69 (01) :53-70
[6]   The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation [J].
Chae, Kyung C. ;
Lim, Dae E. ;
Yang, Won S. .
PERFORMANCE EVALUATION, 2009, 66 (07) :356-367
[7]   Factorization and Stochastic decomposition properties in bulk queues with generalized vacations [J].
Chang, SH ;
Takine, T .
QUEUEING SYSTEMS, 2005, 50 (2-3) :165-183
[8]   Analysis of the discrete-time bulk-service queue Geo/GY/1/N+B [J].
Chaudhry, ML ;
Chang, SH .
OPERATIONS RESEARCH LETTERS, 2004, 32 (04) :355-363
[9]  
CHOI BD, 1994, J OPER RES SOC JPN, V37, P171
[10]   Tail distribution of the delay in a general batch-service queueing model [J].
Claeys, Dieter ;
Steyaert, Bart ;
Walraevens, Joris ;
Laevens, Koenraad ;
Bruneel, Herwig .
COMPUTERS & OPERATIONS RESEARCH, 2012, 39 (11) :2733-2741
123