1. Consider two machines that are maintained by a single repairman. Machine i functions for an exponential time with ratei before breaking down, i = 1,2. The repair times (for either machine) are exponential with rate . Can we analyze this as a birth and death process?

2. Consider two machines that are maintained by a single repairman. Machine i functions for an exponential time with ratei before breaking down, i = 1, 2. The repair times (for either machine) are exponential with rate .

hint :

(i,j) is the states of machine 1 and 2

u if machine is up and running

r if machine is broken and in repair

w if machine is broken but waiting for repair

show the State /transition rate diagram