Prove that, for an M / M / c queueing system in the steady state, ^2=({2-C[c, a]} C[c, a] Ws^2)/

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Step 1: Understand the system and notation.
In an $M/M/c$ queueing system, arrivals follow a Poi

Prove that, for an $M / M / c$ queueing system in the steady state, $$ \sigma_q^2=\frac{\{2-C[c, a]\} C[c, a] W_s^2}{c^2(1-\rho)^2} . $$ Hint: Use the fact that $$ \int_0^{\infty} x^n e^{-\mu x} d x=n ! \mu^{-n-1} . $$