A company has three telephone lines. Incoming calls are generated by the customers according

to a Poisson process with mean rate of 20 calls per hour. Calls that find all telephone lines

busy are rejected and those calls that are able to get through will be served for a length of

time that is exponentially distributed with mean 4 minutes. Let the number of busy lines

be the state of the system. Write down the Markov chain and the generator matrix for this

system. Hence solve the steady-state probability distribution for the system. (10mks)