IJPAM: Volume 50, No. 3 (2009)

SEMIGROUP APPROACH OF A REPAIRABLE
QUEUEING SYSTEM WITH THREE KINDS OF STATES

Muyidin Helil$^1$, Geni Gupur$^2$, Rena Ehmet$^3$
$^{1,2,3}$College of Mathematics and Systems Science
Xinjiang University
Urumqi, 830046, P.R. CHINA
e-mail: [email protected]


Abstract.By using the Hille-Yosida Theorem, Phillips Theorem and Fattorini Theorem in functional analysis, we will prove that a repairable queueing system with three kinds of states has a unique positive time-dependent solution that satisfies probability condition.

Received: September 12, 2007

AMS Subject Classification: 47D03

Key Words and Phrases: $C_0$-semigroup, dispersive operator, conservative operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 3