Markovian Queueing Model with Single Working Vacation and Server Breakdown

Abstract

In this article, we investigate a Markovian queuing model with server breakdown and Single working vacation. Arrival follows Poisson process with parameter λ. Service while the single working vacation epoch, normal working epoch together with vacation epoch are all exponentially assigned with rate µb, µv and ηrespectively. After taking first vacation the server wait idle in the system to serve. This type of vacation is called Single Working Vacation (SWV). If the queue length increases, service rate changes from slow rate to normal rate. When the server may subject to sudden breakdown with rate α and after it should be repaired and goes to normal service with rate β. This queue model has been analysed with the help of Matrix Geometric Method (MGM) to find steady state probability vectors. Using it some performance measure is also determined.