A probability model for computer system overhead

Two models for computer system overhead are developed by considering the number of jobs in the system as an immigration-death process. The models developed relate the death rates to the state of the process. The first model uses the total numver of jobs in the system as the state of the processe. The second model classifies the jobs in the system according to the priority classes unsed in the computer system.In the model based on the total number of jobs in the system, the death rate when the system is in the state i, μ_i, is μ_i = μ min(i, x₀) where μ and x₀ are parameters to be estimated by maximum likelihood. In the second model, the death rate for jobs in the k^th priority class when the state of the system is i = (i₁…,i_p), μ_i^(k) is given by $\text{μ}{}_{\mathrm{i}}{}^{\mathrm{(k)}}\text{=μ}{}^{\mathrm{(k)}}\text{i}{}_{\mathrm{k}}\text{min}\text{(1,}\text{x}{}_0\text{i·1}\text{)}$. Computational difficulties in finding the maximum likelihood estimates of the parameters for this model are noted.