(solution) Consider a finite-capacity G/M/1 queueing that allows at most 3 customers in the system including…

(solution) Consider a finite-capacity G/M/1 queueing that allows at most 3 customers in the system including…

Consider a finite-capacity G/M/1 queueing that allows at most 3 customers in the system including the customer receiving service. The time to serve a customer is exponentially distributed with mean 1/μ. As usual, let rn denote the probability that n customers are served during an interarrival time, n = 0, 1, 2, 3, and let fA(t) be the PDF of the interarrival times. Find rn in terms of μ and MA(s), where MA(s) is the s-transform of fA(t).