Discussion
Let \(L_{q}\) be the average number of customers in the queue, \(\lambda\) be the customer arrival rate and \(\mu\) be the average service rate. Then average waiting time for a customer in the queue for all infinite source queueing models is :
Answer: D
The average waiting time in the queue is \(L_{q}/\lambda\).
Little's law applied to the queue alone states \(L_{q} = \lambda W_{q}\): the average number waiting equals the arrival rate times the average wait. It holds for any infinite-source queue in steady state, whatever the arrival and service distributions. So \(W_{q} = L_{q}/\lambda\).
\(L_{q}/\mu\) divides by the wrong rate. \(\lambda/\mu\) is the traffic intensity \(\rho\), a pure number, and \(\mu/\lambda\) is its reciprocal; neither is a time.
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