IJPAM: Volume 85, No. 6 (2013)

FURTHER RESEARCH ON THE M/M/1 RETRIAL
QUEUEING MODEL WITH SPECIAL RETRIAL TIMES

Aidahong Abulimaiti1, Geni Gupur2
1,2College of Mathematics and Systems Science
Xinjiang University
Urumqi, 830046, P.R. CHINA


Abstract. We study the spectrum of the underlying operator which correspondents to the M/M/1 retrial queueing model with special retrial times and obtian that all
$\eta\in\left(-\lambda,\frac{-(2\lambda+\alpha+\beta)+\sqrt{(\alpha+\beta)^2+4\lambda\beta}}{2}\right)$
are eigenvalues of the underlying operator with geometric multiplicity one.

Received: June 25, 2013

AMS Subject Classification: 47A10

Key Words and Phrases: the M/M/1 retrial queueing model with special retrial times, eigenvalue, geometric multiplicity

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DOI: 10.12732/ijpam.v85i6.12 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 6