Timeline for A question about intuition of fluid limit in queuing system
Current License: CC BY-SA 3.0
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| May 30, 2016 at 7:25 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| May 30, 2016 at 5:23 | comment | added | KevinKim | So your answer indicates that $\pi_1(t)$, i.e., the fraction of queue with EXACTLY one people, should be 0 as $N\rightarrow\infty$, right? But when I run a simulation, it seems that $\pi_1(t)\rightarrow \lambda t$. I think I want to make a clarification. If we let $Q_1(t)$ be the queue length process at server 1, then I agree, if you do the scaling $\frac{1}{N}Q(t)$, then as $N\rightarrow\infty$, then this stuff becomes continuous. But, $\pi_1(t)$ is not $\frac{1}{N}Q(t)$. So I guess, in my problem, there is no "scaling" as in the "fluid limit". I guess my case should not be called fluid limit | |
| May 30, 2016 at 5:05 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |