queueing system

 An airline ticket office has two ticket agents answering incoming calls for flight reservations; each agent is paid $12 per hour. The phone system allows one caller to be put on “hold” until an agent is available to take the call. If all three phone lines (both agent lines and the hold line) are busy, a potential customer gets a busy signal, and it is assumed they call a competitor and their business is lost. Calls and attempted calls occur randomly (i.e., according to a Poisson process) at a mean rate of one per minute. The length of a telephone conversation has an exponential distribution with mean of ½ minutes. Consider that every interaction with a customer has an expectation of $10 profit while potential customers lost to a competitor represent a $10 lost opportunity. 

a.  Describe this queueing system and provide the system diagram. 

b.  Find the steady state probabilities for this system. 

c. What is the 8-hour work day profit for this office? 

d.  Would you recommend hiring one more agent to answer calls? Explain your answer.