(Solved): Consider a two-server parallel queuing system where customers arrive according to a Poisson process ...

Consider a two-server parallel queuing system where customers arrive according to a Poisson process with rate \( \lambda \), and where the service times are exponential with rate \( \mu \). Moreover, suppose that arrivals finding both servers busy immediately depart without receiving any service (such a customer is said to be lost), whereas those finding at least one free server immediately enter service and then depart when their service is completed. (a) If both servers are presently busy, find the expected time until the next customer enters the system. (b) Starting empty, find the expected time until both servers are busy. (c) Find the expected time between two successive lost customers.