I am studying various parameters related to queueing models. Does $M/M/1$ have lesser delay compared to $M/G/1$? I think yes. Can anyone verify this? How does this compare to $G/M/1$? Anyone have any resources that I can read?
2026-03-28 22:37:42.1774737462
Statisitics for queueing models
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The mean response time in an M/M/1 queue with arrivals at rate $\lambda$ and service at rate $\mu$ is
$$\frac{1}{\mu-\lambda}$$
while in an M/G/1 queue with arrivals at rate $\lambda$ and service time distribution $S$ with $\mathbb E(S)=1/\mu$
$$\frac{\rho + \lambda \mu \text{Var}(S)}{2(\mu-\lambda)} + \frac{1}{\mu}$$
where $\rho=\lambda/\mu$. I don't have a formula for the G/M/1 queue to hand. We cannot write an an inequality between these two results above, it depends on the values of $\lambda$, $\mu$ and the variance of $S$. Are you interested in any particular cases?