(Erlang’s Loss System) Each operator at the customer service department of an airline can serve only one call. There are c operators, and the incoming calls form a Poisson process with rate λ. The...

(Erlang’s Loss System) Each operator at the customer service department of an airline can serve only one call. There are c operators, and the incoming calls form a Poisson process with rate λ. The time it takes to serve a customer is exponential with mean 1/µ, independent of other customers and the arrival process. If all operators are busy serving other customers, the additional incoming calls are rejected. They do not return and are called lost calls.

(a) In the long-run, what proportion of calls are lost?

(b) Suppose that λ = µ. How many operators should the airline hire so that the probability that a call is lost is at most 0.004?