# Question

Consider the birth-and-death process with the following mean rates. The birth rates are λ0 = 2, λ1 = 3, λ2 = 2, λ3 = 1, and λn = 0 for n > 3. The death rates are μ1 = 3, μ2 = 4, μ3 = 1, and μn = 2 for n > 4.

(a) Construct the rate diagram for this birth-and-death process.

(b) Develop the balance equations.

(c) Solve these equations to find the steady-state probability distribution P0, P1, . . . .

(d) Use the general formulas for the birth-and-death process to calculate P0, P1, . . . . Also calculate L, Lq, W, and Wq.

(a) Construct the rate diagram for this birth-and-death process.

(b) Develop the balance equations.

(c) Solve these equations to find the steady-state probability distribution P0, P1, . . . .

(d) Use the general formulas for the birth-and-death process to calculate P0, P1, . . . . Also calculate L, Lq, W, and Wq.

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