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9

You have fallen victim to the renewal paradox, a.k.a. inspection paradox, a.k.a. length-biased sampling. $F_{\Delta}$ is the distribution of service time for the kth customer, but it is NOT the distribution of service time for the customer being served at a preselected time $T$. The very manner of selecting the customer based on observing at a preselected ...

4

Note: This answer is intended to show what I have learned from the valuable answer provided by @Mark L.Stone. His post answered my question of why the simulation is biased. Hence, this post provides only additional insight. I chose to post it as an answer and not an edit due to the original question already being lengthy. What has been learned comes from ...

4

I have never encountered a problem like this in literature, but here is one possible way of formulating the problem as a MIP. Notation: $n$: length of the number series $l$: desired length of the subsequence $q_i$: number at position $i$ in the original number series ($i \in I = \{1,\ldots,n\}$) $r_j$: number at position $j$ in the subsequence (\$j \in J = \{...

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