DefinePK

Abstract

This paper investigates the queuing system with multiple vacation, correlated servers, feedback and catastrophes. Inter arrival times follow an exponential distribution with parameters λ and service times follow Bivariate exponential distribution BVE (μ, μ, ν) where μ is the service time parameter and ν is the correlation parameter. Both the servers go on vacation with probability one when there are no units in the system. Laplace transform approach has been used to find the time-dependent solution. The model estimates the total expected cost, total expected profit and obtained the optimal values by varying time for cost and profit. The best optimal value at t=5 when service rate=2.75 and t=2 when feedback probability=0.55 for minimum cost and maximum profit respectively.  These important key measures give a greater understanding of the model behaviour. Numerical analysis and graphical representations have been done by using Maple software.