An important unit consists of two components placed in parallel. The unit performs satisfactorily if one of the two components is operating. A component breaks down in a given period with probability q. Assume that the component breaks down only at the end of a period. When this occurs, the parallel component takes over, if available, beginning at the next period. Only one servicewoman is assigned to service each component in need of repair, and it takes two periods to complete the servicing.

a) Model the situation described above as a Markov chain. Provide your state definition, state space and transition probability matrix.

b) What is the probability that there is a waiting line of length 1 (a component needing service but not being worked on) at the end of a current period?

c) What are the steady state probabilities?

d) If it costs $30,000 per period when the unit is inoperable (both components down) and

zero otherwise, what is the expected average cost per period?