Buffered Versus Unbuffered Tree Networks for Accessing a Critical Resource
Buffered Versus Unbuffered Tree Networks for Accessing a Critical Resource
Paul G Spirakis
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Protocol B; (For each node) During each time unit: (1) If the node holds a packet, it sends the packet up one level (2) Receive packets from lower level (if any) (3) If there are more than one packets received, then abort all but one of them. Here we assume that the aborted packets are (ideally) resubmitted h^. Y. -. 'i'f. -rf ■■, '-'■ '■' i ll'iliO Si'-. I -A- at their orip. In nodes, ImmedJ. AteJ. Y after abortion. In practice, either the netu'ork has to notify the origin nodes that their pac...kets were aborted (in which case we need a buffered scheme for the notifications) or the origin nodes time-out the packets sent. (Here, it is usualiy the case that the packets which access the critical resource can travel the tree backwards, without conflicting v;ith up-going packets). If packet p. Does not return after 2 log N time units, then the leaf node tj resubmits it. We shall provide analyses of both the ideal protocol B and its implementation using timeouts. 2. Analysis of the buffered case Let T^(N) be the number of time units needed for all N packets to arrive to the critical resource, passing through a tree of height h.
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