IJPAM: Volume 69, No. 3 (2011)

ASYMPTOTIC BEHAVIOR OF THE TIME-DEPENDENT
SOLUTION OF THE M/M/1 QUEUEING MODEL
WITH OPTIONAL SECOND SERVICE

Alim Mijit$^1$, Geni Gupur$^2$
$^{1,2}$College of Mathematics and Systems Science
Xinjiang University
Urumqi, 830046, P.R. CHINA
$^1$e-mail: genigupur@yahoo.cn
$^2$e-mail: geni@xju.edu.cn


Abstract. By studying the spectral properties of the underlying operator corresponding to the M/M/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution.

Received: January 18, 2011

AMS Subject Classification: 47A10, 47D03, 60K25

Key Words and Phrases: M/M/1 queueing model with optional second service, eigenvalue, resolvent set

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 3