I'm having some issues with a service system where customers arrive randomly, following a Poissonprocess. The lengths in time that customers spend in service are independent and Weibull distributed with the parameters α > 0 and β > 0.
We are testing two different values of β - 1 and 2 - and get two very different behaving queues. My question is how does β actually affect the behaviour of the queue and why? When β = 1 , the queue becomes a M/G/∞ queue, is this why the behaviours are different or how does it really work?
Thanks and I excuse my bad language