IJPAM: Volume 63, No. 4 (2010)

TIME-DEPENDENT ANALYSIS FOR THE $M^{[X]}/G/1$ RETRIAL
QUEUEING MODEL WITH SERVER BREAKDOWNS AND
CONSTANT RATE OF REPEATED ATTEMPTS

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


Abstract.By using the Hille-Yosida Theorem, Phillips Theorem and Fattorini Theorem we prove that the $M^{[X]}/G/1$ retrial queueing model with server breakdowns and constant rate of repeated attempts has a unique nonnegative time-dependent solution which satisfies probability condition.

Received: April 3, 2010

AMS Subject Classification: 47D03, 60K25

Key Words and Phrases: $M^{[X]}/G/1$ retrial queueing model, server breakdowns and constant rate of repeated attempts, $C_0-$semigroup, dispersive operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 4