Modelling the performance of computer mirroring with difference queues

The paper describes modelling of the performance of a special case of two computer systems operating in parallel: computer mirroring. In computer mirroring one of the systems is identified as the main and the other as the backup computer; both computers execute the same tasks. Each system operates independently and consists of an execution unit and a queue of tasks. Task scheduling and execution are modelled as Poisson processes. The performance of the mirroring system is modelled as a difference queue. The conditions for and the steady state solution for the performance of the computer mirroring system are derived. The processing rate μ₂ of the backup system in computer mirroring should be no less than the product of the processing rate μ ₁ of the main system and the utilization rate ρ₁ of the main system, i.e. ρ₁μ₁<μ₂