Suppose that we modify the M/M/2 queueing system as follows: when a server is free, he assists (if needed) the other server, so that the service time, S, has an exponential distribution with parameter 2μ. If a new customer arrives while a customer is being served by the two servers at the same time, then one the servers starts serving the new customer.
(a) Calculate the limiting probabilities if we suppose that A μ.
(b) Suppose that the system capacity is c = 2 and that λ = μ1. Calculate the average number of customers in the system in stationary regime, given that the system is not full.