12.14 In a network queue transmission packets go through two consecutive processes. Router A processes the packets in a time distributed with a geometric distribution with mean 10 ms. Router B routs the packets in a time distributed as a Geometric(20) random variable (also in milliseconds). All the packets need to go through router A and then router B, and we assume there is no shortage of packets for the first queue (immediately after router A processes a packet there is another one in line entering service). Give a graph of the Markov chain describing the states of the two routers.

a) What is the probability for each router being in use?

b) What is the probability that both routers are in use simultaneously?

Hint: look at the stationary distribution.