Steady state M/ M/ 1 Queue

• prob(n) = (___)n prob(0) = _n prob(0)

• _ _n prob(0) = 1 = prob (0) * 1/ (1-_)

• => prob(n) = _n (1 - _)

• avg length = L = _ n prob(n) = _ n (___)n (1-(___))

• L = (1-__ [_ * ( 1 - _ )-2] = __/ ( 1 - _ )

• avg wait W = (1/ µ)L = (1/ µ) __/ ( 1 - _ )

• average time in the system T = W + (1/µ) = 1/ (µ - __

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