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.

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

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


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

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

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