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 ...