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No, you have to build your model empirically with data. Suppose $p(x)$ denotes the probability of cancel in front of you when your order is positioned $0 \leq x \leq 1$ through the queue, there are a few trivial cases: If you just joined the queue, any reduction in depth at the level must come from in front, i.e. $p(x=1)=1$ If you are at the front of the ...

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