Question: 48. Consider an n-server parallel queuing system where customers arrive according to a Poisson process with rate , where the service times are exponential random

48. Consider an n-server parallel queuing system where customers arrive according to a Poisson process with rate λ, where the service times are exponential random variables with rate μ, and where any arrival finding all servers busy immediately departs without receiving any service. If an arrival finds all servers busy, find

(a) the expected number of busy servers found by the next arrival,

(b) the probability that the next arrival finds all servers free,

(c) the probability that the next arrival finds exactly i of the servers free.

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