Gregory Lauer (glauer@SURAN.BBN.COM)
05 Oct 87 15:40:34 EDT (Mon)
transmissions. Thus in this example, hop-by-hop acks not only reduce the
umber of transmissions required but also reduce the variance in the number of
transmissions required (making it easier to have a good estimate of the
round-trip time, and thus reducing the number of unnecessary retransmissions).
For networks with lower losses, the overhead of the hop-by-hop acks will
outway the reduction in number of transmissions required. We can get an upper
bound on when hop-by-hop acks help as follows. An upper bound on the number of
transmissions required without hop-by-hop acks is N/(1-p)**N (i.e. each failed
transmission takes the maximum number of hops plus 1). A lower bound on the
number required with hop-by-hop acks is 2N/(1-p) (i.e. never retransmit a
packet once it has been received...even if you don't know it's been received).
Equating these yields the fact that hop-by-hop acks don't help if
p<1-(.5)**[1/(N-1)], which for N=10 corresponds to p<.074.
This type of analysis is perhaps appropriate for a packet radio network, where
there may be a significant probability that a radio just doesn't receive the
packet and one can (maybe) argue that the probability of loss is independent
from node to node and from transmission to transmission. This type of analysis
is less useful in networks where packet loss is due to congestion (and
corresponding buffer shortages), where acks have a higher priority, where there
is likly to be significant correlation between the probability that nodes are
congested and where packet (re)transmission is due mainly to timers going off
before a node has a chance to ack a packet that it correctly received.
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