Functionally identical machines are available from N different vendors. The lifetimes of the machines from vendor i are iid exp(i) random variables. The machines from different vendors are independent of each other. We use a "cyclic" replacement policy parameterized by a fixed positive number T as follows: suppose we are currently using a machine from vendor i. If it is less than T time units old upon failure, it is replaced by a machine from vendor i + 1 if i < N and vendor 1 if i = N. If the machine is at least T time units old upon failure, the replacement is from vendor i. Replacements are instantaneous. Let X(t) = i if the machine in use at time t is from vendor i.

1. Is {X(t), t 0} an SMP? If it is, give its kernel G.

2. What is the long run fraction of the time that a machine from vendor i is in use?

3. Suppose a machine from vendor i costs $ci. What is the long run cost per unit

time of operating this policy?