Reconsider Prob. 16.6-2. Now suppose that the manufacturer keeps a spare machine that only is used when
Question:
Reconsider Prob. 16.6-2.
Now suppose that the manufacturer keeps a spare machine that only is used when the primary machine is being repaired. During a repair day, the spare machine has a probability of 0.1 of breaking down, in which case it is repaired the next day. Denote the state of the system by (x, y), where x and y, respectively, take on the values 1 or 0 depending upon whether the primary machine (x) and the spare machine (y) are operational (value of 1) or not operational (value of 0) at the end of the day. [Hint: Note that (0, 0) is not a possible state.]
(a) Construct the (one-step) transition matrix for this Markov chain.
(b) Find the expected recurrence time for the state (1, 0).
Step by Step Answer:
Introduction To Operations Research
ISBN: 9780072321692
7th Edition
Authors: Frederick S. Hillier, Gerald J. Lieberman