16. Consider a 2 server system where customers arrive according to a Poisson process with rate λ, and where each arrival is sent to the server currently having the shortest queue. (If they have the same length queue then the choice is made at random.) The service time at either server is exponential with rate μ, whereI mage. For , say that the state isI mage if both servers currently have n customers, and say that the state isI mage,I mage, if one of the servers has n customers and the other has m.

(a) Write down the balance equation equating the rate at which the process enters and leaves a state for state Image.

(b) Write down the balance equations equating the rate at which the process enters and leaves states of the form , Image.

(c) Write down the balance equations for the states Image, .

(d) Write down the balance equations for the states Image , Image.

(e) In terms of the solution of the balance equations, find the average time a customer spends in the system.