0
$\begingroup$

I know the exit rate ($\mu$) and the average waiting time in the queue ($W_q$). I need solve to rate of input ($\lambda$) in a queue.

$\rho = \frac{\lambda}{c\mu} < 1$

$\pi_0 = \left[\left(\sum_{k=0}^{c-1}\frac{(c\rho)^k}{k!} \right) + \frac{(c\rho)^c}{c!}\frac{1}{1-\rho}\right]^{-1}$

$W_q=\frac{1}{(c-1)!}\left(\frac{\lambda}{\mu}\right)^c\pi_0\frac{\mu}{(c\mu-\lambda)^2}$

But I do not know how to solve this sum. Is there a simple analytical solution?

$\endgroup$
  • $\begingroup$ Why not just add up the $c$ values $(c\rho)^k/k!$? $\endgroup$ – jbowman Jan 29 at 17:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.