A maintenance person has the job of keeping two machines in working order. The amount of time that a machine works before breaking down has an exponential distribution with a mean of 10 hours. The time then spent by the maintenance person to repair the machine has an exponential distribution with a mean of 8 hours.
(a) Show that this process fits the birth-and-death process by defining the states, specifying the values of the λn and λn, and then constructing the rate diagram.
(b) Calculate the Pn.
(c) Calculate L, Lq, W, and Wq.
(d) Determine the proportion of time that the maintenance person is busy.
(e) Determine the proportion of time that any given machine is working.