Browse > Article
http://dx.doi.org/10.14317/jami.2015.343

TAIL ASYMPTOTICS FOR THE QUEUE SIZE DISTRIBUTION IN AN MX/G/1 RETRIAL QUEUE  

KIM, JEONGSIM (Department of Mathematics Education, Chungbuk National University)
Publication Information
Journal of applied mathematics & informatics / v.33, no.3_4, 2015 , pp. 343-350 More about this Journal
Abstract
We consider an MX/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the MX/G/1 retrial queue.
Keywords
MX/G/1 retrial queue; tail asymptotics; queue size distribution;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 S.A. Grishechkin, Multiclass batch arrival retrial queues analyzed as branching process with immigration, Queueing Systems 11 (1992), 395-418.   DOI
2 J. Kim, B. Kim and S-S. Ko, Tail asymptotics for the queue size distribution in an M/G/1 retrial queue, J. App. Probab. 44 (2007), 1111-1118.   DOI
3 V.G. Kulkarni, Expected waiting times in a multiclass batch arrival retrial queue, J. Appl. Probab. 23 (1986), 144-154.   DOI
4 V.G. Kulkarni and L.H. Liang, Retrial queues revisited, In: Frontiers in Queueing: Models and Applications in Science and Engineering (J.H. Dshalalow, ed.), CRC Press, Boca Raton, 1997, 19-34.
5 W. Shang, L. Liu and Q. Li, Tail asymptotics for the queue length in an M/G/1 retrial queue, Queueing Systems 52 (2006), 193-198.   DOI
6 Y.W. Shin and D.H. Moon, On approximations for GI/G/c retrial queues, J. Appl. Math. & Informatics 31 (2013), 311-325.   DOI
7 K. Yamamuro, The queue length in an M/G/1 batch arrival retrial queue, Queueing Systems 70 (2012), 187-205.   DOI
8 T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987), 201-233.   DOI
9 J.R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990-1999, Top 7 (1999), 187-211.   DOI
10 J.R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Model. 30 (1999), 1-6.   DOI
11 J.R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000-2009, Math. Com-put. Model. 51 (2010), 1071-1081.   DOI
12 J.R. Artalejo and A. Gómez-Corral, Retrial Queueing Systems, Springer, 2008.
13 G.I. Falin, Aggregate arrival of customers in a one-line system with repeated calls, Ukrainian Mathematical Journal 28 (1976), 437-440.   DOI
14 G.I. Falin, On a multiclass batch arrival retrial queue, Adv. Appl. Probab. 20 (1988), 483-487.   DOI
15 G.I. Falin, A survey of retrial queues, Queueing Systems 7 (1990), 127-168.   DOI
16 G.I. Falin and J.G.C. Templeton, Retrial Queues, Chapman & Hall, London, 1997.