• THE RELIABILITY ANALYSIS OF M/G/1 RETRIAL QUEUEING SYSTEM FOR THIRD OPTIONAL SERVICE SUBJECT TO SERVER BREAKDOWN AND REPAIR

DR. R. K. SHRIVASTAVA, ROHIT SINGH TOMAR*

Abstract


In this paper we are analysing the reliability analysis of third optional service for a single server retrial queueing system subject to server breakdowns occurs randomly at any phase of service. Arrival of passengers follows the Poisson’s distribution law with parameter λ, while the servers serving their services (parameter µ) using exponential distribution law on the basis of FCFS discipline. This exponential distribution rate comes to fail at second phase and third optional phase of service. We also derive the joint probability distribution for the server, the probability generating function of the stationary queue size distribution, some important performance measures and reliability analysis with a numerical example. We obtain the transient and the steady state solutions for both queueing and reliability measures, by using a supplementary variable method.


Keywords


The reliability analysis, optional service, server breakdown and repair, M/G/1 queue, stationary queue size distribution and reliability index.

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