Abstract
A retrial single-server queueing model with two types of customers is considered. Arrivals occur according to the Marked Markovian Arrival Process (MMAP). In case of the server occupancy at the arrival epoch, the customer moves to the orbit depending on the type of the customer. One orbit is an infinite while the second one is a a finite. Service time distributions are exponential with the parameter depending on the type of a customer. Joint distribution of the number of customers in the orbits and some performance measures are computed. Numerical results are presented. Possible extensions of the model are outlined.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Artalejo, J.R., Comez-Corral, A.: Retrial queueing systems: a computational approach. Springer, Heidelberg (2008)
Domenech-Benlloch, M.J., Gimenez-Guzman, J.M., Pla, V., Casarea-Giner, V., Martinez-Bauset, J.: Solving multiserver systems with two retrial orbits using value extrapolation: a comparative perspective. In: Al-Begain, K., Fiems, D., Horváth, G. (eds.) ASMTA 2009. LNCS, vol. 5513, pp. 56–70. Springer, Heidelberg (2009)
Dudin, S.A.: The MAP/N/N retrial queueing system with time-phased batch arrivals. Problems of Information Transmissions 45, 270–281 (2009)
Gomez-Corral, A.: A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Annals of Operations Research 141, 163–191 (2006)
He, Q.M.: Queues with marked customers. Advances in Applied Probability 28, 567–587 (1996)
Klimenok, V.I., Dudin, A.N.: Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory. Queueing Systems 54, 245–259 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Avrachenkov, K., Dudin, A., Klimenok, V. (2010). Retrial Queueing Model MMAP/M 2/1 with Two Orbits. In: Vinel, A., Bellalta, B., Sacchi, C., Lyakhov, A., Telek, M., Oliver, M. (eds) Multiple Access Communications. MACOM 2010. Lecture Notes in Computer Science, vol 6235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15428-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-15428-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15427-0
Online ISBN: 978-3-642-15428-7
eBook Packages: Computer ScienceComputer Science (R0)