Repairable queue with non-exponential service time and variable breakdown rates

Koh, Siew Khew and Pooi, Ah Hin * and Tan, Yi Fei (2015) Repairable queue with non-exponential service time and variable breakdown rates. In: Proceedings of International Conference on Mathematics, Engineering and Industrial Applications 2014 (ICoMEIA 2014) (28–30 May 2014), Penang, Malaysia. AIP Conference Proceedings (1660). AIP Publishing, Melville, NY, 050026-1.

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Abstract

Consider a single server queue in which the service station may breakdown according to a Poisson process with rates γ in busy time and γ’ in idle time respectively. After a breakdown, the service station will be repaired immediately and the repair time is assumed to have an exponential distribution with rate δ. Suppose the arrival time has an exponential distribution with rate λ, and the probability density function g(t) and the cumulative distribution function G(t) of the service time are such that the rate g(t)/[1 – G(t)] tends to a constant as t tends to infinity. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution of the system

Item Type: Book Section
Additional Information: First author is with Faculty of Engineering and Science, UTAR; 2nd author is with Sunway University Business School; 3rd author is with Faculty of Engineering, Multimedia University
Uncontrolled Keywords: Service time; constant asymptotic rate; stationary queue length distribution
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Sunway University > Sunway University Business School > Dept. Financial Mathematics & Statistics
Depositing User: Ms. Molly Chuah
Date Deposited: 28 Mar 2016 06:04
Last Modified: 28 Mar 2016 06:04
URI: http://eprints.sunway.edu.my/id/eprint/311

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