(46) into Eq.
(44). In the derivation of Eq. (46), we have made use of the fact that the probability that a
frame found in backoff stage i is ultimately dropped, is given by the probability that it first
Performance Study of IEEE 802.11 DCF and IEEE 802.11e EDCA 84
reaches the backoff stage R (i.e., it collides for R-i times), and then it also collides during
the last transmission attempt. Hence P{LOSS|s=i}=pR+1-i.
The average delay expression can be further simplified. From Eq. (33), the probability
of a successful transmission, expressed in Eq. (10), can be rewritten as:
(47)
Hence, recalling that the throughput S was computed in Eq. (12) as the probability of
successful transmission multiplied by the ratio E[P]/E[slot],
(p
N Psuccess ??’ = 1 ) ?„
(48)
This final expression has an elegant intuitive interpretation11. From Little??™s Result, the
first term represents the average inter-departure time between two successfully delivered
frames from the same station. This differs from the average access delay as, between two
successful transmissions, a number of dropped frames may occur. Now, pR+1 represents the
probability that a new frame entering the system (i.
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