On abstract stochastic differential equation in hilbert spaces with dissipative drift

A multi–operative Markovian machine interference model with arbitrary inital number of breakdowns is studied by taking mean breakdown of each machine as λ^-1 and the mean repairtime of each machine as μ^-1. The transient state probabilities of number of breakdowns and initial busy period distributions of a given number of operatives have been obtained in closed form using Laplace transform and matrix theory. The efficacy of the method is tested by computing the state probabilities and measures of effectiveness such as machine availability function and operating efficiency function for various values of traffic intensity ρ=λ/μ.