On October 02, 2003 07:47 pm, Martin Stone Davis wrote:
Ian Clarke wrote:
I still don't have my head around this fully yet, but I think the core flaw in your proposal is that it assumes that, for a given key, the pSuccess values of repeated requests to the same node are independent, but they are not. After the first failure, pSuccess for that node drops to 0.
Hand-wavy explanation: When trying to ask "how long will it take this one node to give us a 1 unit of data?" we don't have to be concerned about how our opinions about pSuccess will change in the future. All that matters is the true value itself. Since we don't know the true value, the best we can do is use our current opinion of the true value.
Admission of guilt: As I wrote it, pSuccess is a bit ambiguous: is it the current (and changing) estimate of how likely future successes will be? or is it the "true" (and static) chance of success? If the former, then we'd write it with a little hat on top. If the latter, we'd probably use a greek symbol for it. Since I didn't do a very mathematically sound derivation, it would be problematic to discuss your concern here in detail.
pSuccess is a function of (node,key). It will vary for a give node depending on the key passed. This is what worries Ian about your suggestions. Also we do not just use tFailure. The term is (tFailure+tToDoThisOnAnotherNode(key))
Ian, is this what your worry is? I don't get it. I thought that we are estimating time to retrieve a fixed key. In which case, it doesn't matter that pSuccess is a function of (node,key): I hold key fixed and take pSuccess to be only a function of node.
I understand that the tToDoThisOnAnotherNode concept is something I have to take into consideration. That's what I'm trying to work out on paper right now.
-Martin
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