IJPAM: Volume 53, No. 1 (2009)

ON THE ANALYSIS OF M/M/1 FEEDBACK QUEUE WITH
CATASTROPHES USING CONTINUED FRACTIONS

V. Thangaraj$^1$, S. Vanitha$^2$
$^{1,2}$Ramanujan Institute for Advanced Study in Mathematics
University of Madras
Chennai, 600 005, INDIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.A transient solution is obtained analytically using continued fractions for the system size in an M/M/1 feedback queue with the possibility of catastrophes at the service counter. Asymptotic behavior of the probability of the server being idle and mean system size are obtained. The steady state probability of the system size is also presented. Some key performance measures are computed. Busy period and its moments are also obtained. Further numerical illustrations are used to discuss the system performance measures using MAPLE software.

Received: April 16, 2009

AMS Subject Classification: 26A33

Key Words and Phrases: M/M/1 feedback queue with catastrophes, transient analysis, steady state analysis, busy period analysis, mean system size, throughput, continued fraction, MAPLE software

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 1