[chord] Impact of Chord ring size on probability of lookup failure

[Salter JW Mr (PG - Computing)]

Hi there,
 
I am a PhD student at the University of Surrey in the UK, and am looking for a bit of help regarding Chord.
 
If we ignore successor lists and stabilisation, does the size of a Chord ring have any impact on the probability that a lookup will be successful under static failure conditions?  
 
For example, if m lookups were undertaken in a ring of size j and a further m lookups were undertaken in a ring of size k, where j>k, should we expect a larger number of lookups to be successful in the larger/smaller ring?  (Assuming that all nodes in both rings have the same probability of failure and the lookup targets are equally distributed around the ring).
 
I have built some quick simulations to test this.  The proportion, therefore the probability, of successful lookups seems to be constant, independent of the size of the ring.  
 
Does this make sense?  On the one hand, increasing the size of the ring means that an average-case lookup will have to pass through more nodes, meaning the chance of encountering a failed node is higher.  However, the increased size of the ring also means finger tables are larger, offering more possibilities for alternative routes to the target node.  Could this mean the two cancel each other out.
 
Is this what you would expect, or am I missing something about Chord?  Any help, suggestions or pointers would be very much appreciated!
 
Thanks for your time,
James Salter
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