Analysis for a Working Vacation Queue with Batch Service
ZHANG Hongbo1, WANG Hongwei1, SHI Dinghua2
1. School of Statistics and Mathematics, Henan Finance University, Zhengzhou 450046, China; 2. College of Science, Shanghai University, Shanghai 200444, China
Abstract：In this paper, we consider an M/M/1 queue with multiple or single working vacation and batch service both in regular busy period and in working vacation, where the batch size in regular busy period or in working vacation period is assumed to be random variable with different distribution. The queueing system can be modeled by a special GI/M/1 type Markov process. By solving the stationary distribution for the process, we obtain some exact descriptions for the stationary status of the server. We also give the stochastic decomposition structure for stationary queue length of the queue.
张宏波, 王红蔚, 史定华. 对一类批量服务工作休假排队的分析[J]. 应用数学学报, 2020, 43(5): 781-791.
ZHANG Hongbo, WANG Hongwei, SHI Dinghua. Analysis for a Working Vacation Queue with Batch Service. Acta Mathematicae Applicatae Sinica, 2020, 43(5): 781-791.
Doshi B. Queueing systems with vacations-a survey. Queueing Systems, 1989, 1:29-66
[2]
Tian N, Zhang Z. Vacation queueing models-theory and applications. New York:Springer, 2006
[3]
Servi L, Finn S. M/M/1 queues with working vacations (M/M/1/WV). Performance Evaluation, 2002, 50:41-52
[4]
Liu W, Xu X, Tian N. Stochastic decompositions in the M/M/1 queue with working vacations. Operations Research Letters, 2007, 35:595-600
[5]
Tian N, Zhao X, Wang K. The M/M/1 queue with single working vacation. International Journal of Information and Management Sciences, 2008, 19:621-634
[6]
Baba Y. Analysis of a GI/M/1 queue with multiple working vacations. Operations Research Letters, 2005, 33:201-209
[7]
Wu D, Takagi H. M/G/1 queue with multiple working vacations. Performance Evaluation, 2006, 63:654-681
[8]
Li J, Tian N. Performance analysis of a GI/M/1 queue with single working vacation. Applied Mathematics and Computation, 2011, 217:4960-4971
[9]
Gao S, Liu Z. An M/G/1 queue with single working vacation and vacation interruption under Bernoulli schedule. Applied Mathematical Modelling, 2013, 37:1564-1579
[10]
Li J, Zhang Z, TIan N. Analysis for the MX/M/1 working vacation queue. International Journal of Information and Management Sciences, 2009, 20:379-394
[11]
Baba Y. The MX/M/1 queue with multiple working vacation. American Journal of Operations Research, 2012, 2:217-224
[12]
Bailey N. On queueing processes with bulk service. Journal of the Royal Statistical Society, Series B, 1954, 61:80-87
[13]
Jeyakumar S, Senthilnathan B. Steady analysis of bulk arrival and bulk service queueing model with multiple working vacations. International Journal of Mathematics in Operational Research, 2016, 9:375-394
[14]
Jeyakumar S, Senthilnathan B. Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown. RAIRO-Operations Research, 2017, 51:485-508
[15]
Li Q. Constructive computation in stochastic models with applications, the RG-factorizations. Beijing:Tsinghua University Press, New York:Springer, 2010
2020, Vol. 43 
