Abstract
In this paper we study reliability analysis of a k-out-of-n system with a repair facility which provides an essential and several inessential service with given probabilities. At the epoch the system starts, all components are in operational state. Service to failed components are in the order of their arrival. When a component is selected for repair, we assume that the server may select it either for a service that turns out to be different from what is exactly needed for it, which we call the inessential service with the probability p or for desired service, called essential service with probability (1-p). Once the inessential service process starts, a random clock is assumed to start ticking which decides the event to follow: if the clock realises first (still inessential service going on) the components ongoing service is stopped and it is replaced with a new component. On the other hand if the inessential service gets completed before the realisation of the random clock, then the component moves for the essential service immediately. The life-time of a component, the essential service time and the random clock time have independent exponential distributions and the inessential service time is assumed to follow a phase type distribution. The steady state distribution of the system has been obtained explicitly and several important performance measures derived and verified numerically. The extension of the results reported to the case of more than one essential service is worth examining. This has applications in medicine, biology and several other fields of activity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Madan, K.C., Al-Rawi, S.R., Al-Nasser, A.D.: On Mx/(G1G2)/1/G(BS)/Vs vacation queue with two types of general heterogeneous service. J. Appl. Math. Decis. Sci. 3, 123–135 (2005)
Ayyappan, G., Sathiya, K., Subramanian, A.M.G.: M[X]/G/1 Queue with two types of service subject to random breakdowns, multiple vacation and restricted admissibility. Appl. Math. Sci. 7(53), 2599–2611 (2013)
Saravanarajan, M.C., Chandrasekaran, V.M.: Analysis of M/G/1 feedback queue with two types of services, bernoulli vacations and random breakdowns. Int. J. Math. Oper. Res. 6(5), 567–588 (2014)
Acknowledgements
Second and fourth authors acknowledge Department of Science & Technology, Government of India under grant INT/RUS/RMES/P-3/2014 dated 15-4-2015; This research has been financially supported by the Russian Science Foundation (research project No.16-49-02021)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Sathian, M.K., Narayanan, V.C., Vishnevskiy, V., Krishnamoorthy, A. (2016). Reliability of a k-out-of-n System with a Repair Facility – Essential and Inessential Services. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2016. Communications in Computer and Information Science, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-319-51917-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-51917-3_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-51916-6
Online ISBN: 978-3-319-51917-3
eBook Packages: Computer ScienceComputer Science (R0)