Queuing Theory: Computing Delay Probability M/M/C

Question

The delay probability is :

So let's assume that :

λ = 2/3;
μ = 1/3;
c = 3;

How do they arrive by having a queuing delay :

Πw = 0.444 ?

I don't know if I am computing "p" and "Πw" correctly because i never seem to get as close to 0.444.

Answer 1

You have $\rho=\dfrac23$ and $\dfrac{(c\rho)^c}{c!}=\dfrac43$ so your result is $$\Pi_W=\frac{\dfrac43}{\left(1-\dfrac23\right)\left(1+2+2\right)+ \dfrac43}=\frac49\approx 0.444.$$