Repeat Problem 4.3 assuming that arriving customers are assigned to the three servers randomly…

Repeat Problem 4.3 assuming that arriving
customers are assigned to the three servers randomly according to the
respective probabilities a1, a2, and a3, where a1 = a2 + a3 = 1 and ai> 0, i
= 1, 2, 3.

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PROBLEM 4.3

Customers arrive at a three-server facility
according to a Poisson distribution with mean A. If arriving customers are
assigned to each server on a rotational basis, determine the distribution of
interarrival times at each server