The reservation office for Central Airlines has three agents answering incoming phone calls for flight reservations. In addition, one caller can be put on hold until one of the agents is available to take the call. If all four phone lines (both agent lines and the hold line) are busy, a potential customer gets a busy signal, in which case the call goes to another airline. The calls and attempted calls occur randomly (i.e., according to a Poisson process) at a mean rate of 60 per hour. The length of a telephone conversation has an exponential distribution with a mean of 2 minutes.

a. Construct the rate diagram for this queueing system.

b. Find the steady-state probability that

i. A caller will get to talk to an agent immediately,

ii. The caller will be put on hold,

iii. The caller will get a busy signal

c. Find the expected number of busy lines.

d. Find the expected number of busy agents.

e. Find the expected amount of time a customer waiting to talk an agent (i.e. waiting time on the hold line) f. Assume that a customer brings $200 profit if she can get to talk to an agent immediately, $150 profit if she first waits on hold and no profit if she gets a busy signal. What is the average hourly profit of the company?