STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

K. Avrachenkov (), E. Morozov (), R. Nekrasova () and B. Steyaert ()
Additional contact information
K. Avrachenkov: Inria Sophia Antipolis, 2004 Route des Lucioles Sophia Antipolis, 06902, France
E. Morozov: Institute of Applied Mathematical Research, Karelian Research Centre RAS, and Petrozavodsk State University, Russia
R. Nekrasova: Institute of Applied Mathematical Research, Karelian Research Centre RAS, and Petrozavodsk State University, Russia
B. Steyaert: SMACS Research Group, Ghent University, St-Pietersnieuwstraat 41, B-9000 Gent, Belgium

Asia-Pacific Journal of Operational Research (APJOR), 2014, vol. 31, issue 02, 1-18

Abstract: In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate $\mu_{0}^{(i)}$) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

Keywords: Retrial system; constant retrial rate; stability condition; regenerative approach; busy probability; multi-class system (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0217595914400028
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:31:y:2014:i:02:n:s0217595914400028

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0217595914400028

Access Statistics for this article

Asia-Pacific Journal of Operational Research (APJOR) is currently edited by Gongyun Zhao

More articles in Asia-Pacific Journal of Operational Research (APJOR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().