Browse > Article
http://dx.doi.org/10.14403/jcms.2016.29.1.95

AN APPROXIMATION FOR THE QUEUE LENGTH DISTRIBUTION IN A MULTI-SERVER RETRIAL QUEUE  

Kim, Jeongsim (Department of Mathematics Education, Chungbuk National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.29, no.1, 2016 , pp. 95-102 More about this Journal
Abstract
Multi-server queueing systems with retrials are widely used to model problems in a call center. We present an explicit formula for an approximation of the queue length distribution in a multi-server retrial queue, by using the Lerch transcendent. Accuracy of our approximation is shown in the numerical examples.
Keywords
M/M/m retrial queue; queue length distribution; Lerch transcendent;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 M. S. Aguir, O. Z. Aksin, F. Karaesmen, and Y. Dallery, On the interaction between retrials and sizing of call centers, European Journal of Operational Research 191 (2008), 398-408.   DOI
2 M. S. Aguir, F. Karaesmen, O. Z. Aksin, and F. Chauvet, The impact of retrials on call center performance, OR Spectrum 26 (2004), 353-376.   DOI
3 J. R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990-1999, Top 7 (1999), 187-211.   DOI
4 J. R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Model. 30 (1999), 1-6.
5 J. R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000-2009, Math. Comput. Model. 51 (2010), 1071-1081.   DOI
6 J. R. Artalejo, A. Economou, and A. Gomez-Corral, Applications of maximum queue lengths to call center management, Computers & Operations Research 34 (2007), 983-996.   DOI
7 J. R. Artalejo and A. Gomez-Corral, Retrial Queueing Systems, Springer, 2008.
8 A. Erdelyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953.
9 G. I. Falin, A survey of retrial queues, Queueing Systems 7 (1990), 127-168.   DOI
10 G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman & Hall, London, 1997.
11 J. Kim and J. Kim, An approximation for the distribution of the number of retrying customers in an M/G/1 retrial queue, Journal of the Chungcheong Mathematical Society 27 (2014), 405-411.   DOI
12 J. Kim, J. Kim, and B. Kim, Tail asymptotics of the queue size distribution in the M/M/m retrial queue, Journal of Computational and Applied Mathematics 236 (2012), 3445-3460.   DOI
13 V. G. Kulkarni and H. M. 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.
14 T. Yang and J. G. C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987), 201-233.   DOI