Analysis of Two-Dimensional State Markovian Queuing Model with Multiple Vacation, Correlated Servers, Feedback and Catastrophes

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.