Analysis of the machine repair problem: a diffusion process approach

An approximate method based on the diffusion equation is presented for analyzing a non-Markovian machine repair problem. The basic argument used in this approximation is that in the repair stage, the number of failed machines at time t, N(t), is almost always non-empty under heavy-traffic conditions. When time t becomes large, [N(t), t #62; 0] will tend to become a normally distributed random process with appropriate means and variances. With the assumption of normality the estimation of the diffusion parameters becomes tractable, and the method can be used to solve machine repair problems.