This yields:
( ) 1 1 1 ??’ ??’ ??’ = N p ?„ (33)
Eqs. (32) and (32) represent a non linear system in the two unknowns ?„ and p, which
can be solved using numerical techniques.
The above analysis was carried out for general backoff models. By properly choosing
the sequence ??
i and the value R, it can be immediately adapted to more a specific backoff
model, e.g., the binary exponential backoff model adopted in DCF. For example, by
setting:
(34)
??? ??????
??? ??????
??±
?‰?
??’
?‰¤ ?‰¤
??’
=
??· ??·???
??¶
??¬ ??¬??
??«
+
+
=
+ =
??? =
m i W
m i W
CW
CW log m
CW W
R
m
i
i
min
max
min
2
1 2
0
2
1 2
1
1
1
2
??
We model a Binary Exponential Backoff scheme with no retry limit as an upper bound
on the Contention Window (summarized by the value m). Eq. (32) becomes [16]:
Performance Study of IEEE 802.11 DCF and IEEE 802.11e EDCA 80
( )
) ) p ( ( pW ) W )( p (
) p (
W p W p p
m
m i
m i
m i
i i
2 1 1 2 1
2 1 2
2 2 1 1
2
1
0
??’ + + ??’
??’
=
??????
?????? ???
??????
?????? ??±
+ ??’ +
=
??‘ ??‘
??? =
??’
=
?„
(35)
The same DCF Binary Exponential Backoff model, but with a finite retry limit R (for
simplicity of computation, lower than or equal to the parameter m: for the general case
refer to [17]) yields:
) ) p ( )( p ( W ) p )( p (
) p )( p (
R R
R
1 1
1
2 1 1 1 2 1
1 2 1 2
+ +
+
??’ ??’ + ??’ ??’
??’ ??’
= ?„ (36)
4.
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