Consider a birth-and-death process representing a multi-server finite population system with the following birth-and-death rates: k = (4 k) k = 0, 1, 2,

Consider a birth-and-death process representing a multi-server finite population system with the following birth-and-death rates:

λk = (4 − k)λ k = 0, 1, 2, 3, 4

μk = kμ k = 1, 2, 3, 4

a. Find the pk, k = 0, 1, 2, 3, 4 in terms of λ and μ.

b. Find the average number of customers in the system.