Complutense University Library

Markovian retrial queues with two way communication

Artalejo, Jesús R. and Tuan, P.D. (2012) Markovian retrial queues with two way communication. Journal of industrial and management optimization, 8 (4). pp. 781-206. ISSN 1547-5816

[img] PDF
Restricted to Repository staff only until 31 December 2020.

233kB

Official URL: http://www.is.titech.ac.jp/~tuan/papers/Artalejo_Phung-Duc_JIMO12.pdf

View download statistics for this eprint

==>>> Export to other formats

Abstract

In this paper, we first consider single server retrial queues with two way communication. Ingoing calls arrive at the server according to a Poisson process. Service times of these calls follow an exponential distribution. If the server is idle, it starts making an outgoing call in an exponentially distributed time. The duration of outgoing calls follows another exponential distribution. An ingoing arriving call that finds the server being busy joins an orbit and retries to enter the server after some exponentially distributed time. For this model, we present an extensive study in which we derive explicit expressions for the joint stationary distribution of the number of ingoing calls in the orbit and the state of the server, the partial factorial moments as well as their generating functions. Furthermore, we obtain asymptotic formulae for the joint stationary distribution and the factorial moments. We then extend the study to multiserver retrial queues with two way communication for which a necessary and sufficient condition for the stability, an explicit formula for average number of ingoing calls in the servers and a level-dependent quasi-birth-and-death process are derived.


Item Type:Article
Uncontrolled Keywords:Retrial queues; two way communication; blended call centers; stationary distribution; factorial moments; recursive formulae; asymptotic analysis; call centers; customers; model
Subjects:Sciences > Mathematics > Applied statistics
Sciences > Mathematics > Operations research
ID Code:17111
References:

Aksin, Z., Armony, M. and Mehrotra, V. The modern call center: A multi-disciplinary perspective on operations management research. Production and Operations Management 16 (2007), 665-688.

Artalejo, J.R. and Gomez-Corral, A. Steady state solution of a single-server queue with linear repeated request. Journal of Applied Probability 34 (1997), 223-233.

Artalejo, J.R. and Gomez-Corral, A. \Retrial Queueing Systems: A Computational Approach," Springer, Berlin, 2008.

Artalejo, J.R. Accessible bibliography on retrial queues: Progress in 2000-2009. Mathematical and Computer Modelling 51 (2010), 1071-1081.

Artalejo, J.R. and Resing J.A.C. Mean value analysis of single server retrial queues. Asia-Pacific Journal of Operational Research 27 (2010), 335-345.

Avrachenkov, K., Dudin, A. and Klimenok, V. Retrial queueing model MMAP=M2=1 with two orbits . Lecture Note on Computer Science 6235 (2010), 107-118.

Bhulai, S. and Koole, G. A queueing model for call blending in call centers. IEEE Transactions on Automatic Control 48 (2003), 1434-1438.

Choi, B.D., Choi, K.B. and Lee, Y.W. M/G/1 retrial queueing systems with two types of calls and finite capacity. Queueing Systems 19 (1995), 215-229.

Choi, B.D., Kim, Y.C. and Lee, Y.W. The M/M/c retrial queue with geometric loss and feedback. Computers & Mathematics with Applications 36 (1998), 41-52.

Deslauriers, A., L

Deposited On:15 Nov 2012 11:23
Last Modified:27 Nov 2012 08:32

Repository Staff Only: item control page