Discussion
As the variance of service time increases, the waiting time of a customer in \(M|G|1\) queue :
Answer: A
As the service-time variance increases, the waiting time increases.
The Pollaczek-Khinchine formula for the M/G/1 queue gives the mean waiting time in queue as
\[ W_{q} = \frac{\lambda(\sigma^{2} + 1/\mu^{2})}{2(1 - \rho)} \]
where \(\sigma^{2}\) is the variance of service time. With the arrival rate and mean service time fixed, \(W_{q}\) increases linearly with \(\sigma^{2}\). This is why the M/D/1 queue, with constant service, has half the waiting of the M/M/1 queue with the same mean.
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