Three Phases of Service For A Single Server Queueing System Subject To Server Breakdown And Bernoulli Vacation

Rohit Singh Tomar; Dr.R.K.Shrivastav

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P517

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P517

Three Phases of Service For A Single Server Queueing System Subject To Server Breakdown And Bernoulli Vacation

Rohit Singh Tomar, Dr.R.K.Shrivastav

Abstract

This paper deals with an unreliable server having three phases of heterogeneous service on the basis of M/G/1 queueing system. We suppose that customers arrive and join the system according to a Poisson's process with arrival rate λ. After completion of three successive phases of service the server either goes for a vacation with probablity p (0≤ p≤1) or continue to serve the next units, if any, with probablity q(=1 -p). Otherwise it remains in the system until a customer arrives. The server is supposed to be unreliable, hence when the server is working during any phase of service, it may breakdown at any instant and thus service facilty will fail for a short interval of time. Firstly, now we derive the joint probability distribution for the server. Secondly, we derive the probability generating function of the stationary queue size distribution at a departure epoch. Third, we derive Laplace Stieltijes transform of busy period distribution and waiting time distribution. Finally, we obtain some important performance measures and reliability analysis of this model.

Keywords

First phase of service, Second phase of service, Third phase of service, Random breakdowns, Bernoulli vacation, M/G/1 queue, Stationary queue size distribution and reliability index.

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Citation :

Rohit Singh Tomar, Dr.R.K.Shrivastav, "Three Phases of Service For A Single Server Queueing System Subject To Server Breakdown And Bernoulli Vacation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 124-136, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P517