IJPAM: Volume 58, No. 3 (2010)

OTHER EIGENVALUES OF THE M/M/1 RETRIAL
QUEUEING MODEL WITH SPECIAL RETRIAL TIMES

Yusup Ismayil$^1$, Geni Gupur$^2$
$^{1,2}$College of Mathematics and Systems Science
Xinjiang University
Urumqi, 830046, P.R. CHINA
$^2$e-mails: [email protected], [email protected]


Abstract.We prove that for all  $\theta\in(0,1),~\frac{-(2\lambda+\alpha+\beta)+\sqrt{(\alpha+\beta)^2+4\lambda\beta}}{4}{\theta}$  are eigenvalues of the operator corresponding to the M/M/1 retrial queueing model with special retrial times and show: it is impossible that the time-dependent solution of the model exponentially converges to its steady state solution.

Received: December 15, 2009

AMS Subject Classification: 47A10

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 3