IJPAM: Volume 76, No. 1 (2012)

ANALYSIS OF TRANSIENT BEHAVIOUR OF
M/G/1 QUEUE WITH SINGLE VACATION

S. Maragatha Sundari$^1$, S. Srinivasan$^2$
$^1$Department of Mathematics
DMI College of Engineering
Chennai, INDIA
$^2$Department of Mathematics
BSA University
Chennai, INDIA


Abstract. This paper analyses a M/G/1 queue with server vacation on Bernoulli schedule and single vacation policy. The service time follows a general distribution with the density function $M(x)$. The vacation period is exponentially distributed.At the completion of service, the server can take a vacation with probability $p$ or may continue to stay in the system with probability $1-p$. The Laplace Transforms of the probability generating functions of different states of the system have been obtained and the corresponding transient solution of M/G/1 queue is derived.

Received: March 1, 2012

AMS Subject Classification: 60K25

Key Words and Phrases: Poisson arrivals, Bernoulli schedule general service times, server vacation, probability generating function, Laplace transform

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 1