Open AccessRepairable Queue with Non-exponential Interarrival Time and Variable Breakdown Rates
Author(s) -
Koh Siew Khew,
Chin Ching Herny,
Yi Fei Tan,
Pooi Ah Hin,
Goh Yong Kheng,
Min Cherng Lee,
Tan Ching Ng
Publication year - 2018
Publication title -
international journal of engineering and technology
Language(s) - English
Resource type - Journals
ISSN - 2227-524X
DOI - 10.14419/ijet.v7i2.15.11218
Subject(s) - exponential distribution , queue , mathematics , poisson distribution , exponential function , random variable , fork–join queue , constant (computer programming) , statistics , queueing theory , mathematical analysis , computer science , queue management system , computer network , programming language
This paper considers a single server queue in which the service time is exponentially distributed and the service station may breakdown according to a Poisson process with the rates γ and γ' in busy period and idle period respectively. Repair will be performed immediately following a breakdown. The repair time is assumed to have an exponential distribution. Let g(t) and G(t) be the probability density function and the cumulative distribution function of the interarrival time respectively. When t tends to infinity, the rate of g(t)/[1 – G(t)] will tend to a constant. A set of equations will be derived for the probabilities of the queue length and the states of the arrival, repair and service processes when the queue is in a stationary state. By solving these equations, numerical results for the stationary queue length distribution can be obtained.