A system is composed of JV machines. At most M = N can be operating at any one time; the rest are…

A system is composed of JV machines. At most M ≤ N can be operating at any one time; the rest are “spares” . When a machine is operating, it operates a random length of time until failure. Suppose this failure time is exponentially distributed with parameter µ. When a machine fails it undergoes repair. At most JR machines can be ” in repair ” at any one time. The repair time is exponentially distributed with parameter L Thus a machine can be in any of four states: (i) Operating, (ii) ” Up “, but not operating, i.e., a spare, (iii) In repair, (iv) Waiting for repair. There are a total of N machines in the system. At most M can be operating. At most R can be in repair.

” down “. Then the number in repair is min { Y(t), R] and the number waiting for repair is max {0, Y(t) — i?}. The above formulas permit to determine the number of machines in any category, once X(t) is known.