4.2.8 An airline reservation system has a single computer, which breaks down on any given day with probability p. It takes 2 days to restore a failed computer to normal service. Form a Markov chain by taking as states the pairs .x; y/, where x is the number of machines in operating condition at the end of a day and y is 1 if a day’s labor has been expended on a machine, and 0 otherwise. The transition probability matrix is

Compute the system availability .1;0/ for p D 0:01;0:02;0:05, and 0.10.

To state (1,0) (0,0) (0,1) From state (1,0) P=(0,0) q 0 (0, 1) 1 200 P 1 0 0