M/G/M QUEUE WITH TWO STAGE HETEROGENEOUS SERVICE COMPULSORY SERVER VACATION AND RANDOM BREAKDOWNS

V Thangraj

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Advanced Queuing Theory Analysis Reliability and Maintenance Optimization Age of Information Optimization

Abstract

We analyze a single server queue with Poisson arrivals, two stages of heterogeneous service with different (arbitrary) service time distributions subject to random breakdowns and compulsory server vacations with general (arbitrary) vacation periods. After first-stage service the server must provide the second stage service. However, after the completion of each second stage service, the server will take compulsory vacation. The system may breakdown at random and repair time follow exponential distribution. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Also the average number of customers in the queue and the average waiting time are derived.

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References

1986Queueing systems with vacations ? A survey 2001Reliability Analysis of the Retrial Queue with Server Breakdowns and Repairs 1990Retrial queues with server subject to breakdowns and repairs 1998On the single server retrial queue subject to breakdowns 1997A single server queue with service interruptions 2002The Discrete-Time GI/Geo/1 Queue with Multiple Vacations 1999Conditional stochastic decompositions in the M/M/c queue with server vacations 1990Optimal Maintenance Policies for Single-Server Queueing Systems Subject to Breakdowns

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2019Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)2012Analysis of M/G/ 1 queueing model with state dependent arrival and vacation 2014Analysis of M[X]/G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown 2014Mathematical Analysis of Queue with Phase Service: An Overview

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