A model of priority back-up with priority restoration (Q1082724)

The author considers a system of n machines only one of which is being used at any given time. If the one which is currently being used breaks down, it is taken to be repaired while another one takes its place. The repair shop can work on only one machine at any given time. The work (resp. repair) time of the i-th machine is distributed exponentially with parameter \(\lambda_ i\) (resp. \(\mu_ i)\), \(1\leq i\leq n\). There is a priority function \(\sigma\) : \({\mathbb{Z}}_ n\to {\mathbb{Z}}_ n\) which determines the order in which machines are put into use or are being repaired: if machines with indices \(i_ 1,...,i_ k\) are available to work (resp. are to be repaired) then the machine whose index \(i_ s\) yields the minimal value for \(\sigma (i_ s)\) is put into use (resp. is being repaired), \(1\leq s\leq k\). The paper is an analysis of such a system.