e., the average number of backoff slots, plus the single transmission
slot). According to the notation given above:
{ } ) R ,..., ( i
] B [ E
i s | TX P
i i
0
1
1
1
1 ???
+
=
+
= =
??
(30)
In the special case of DCF, a station entering backoff stage i uniformly selects a
backoff value in the range [0,CWi]. Following [16], it is convenient to adopt the notation
Wi=CWi+1. Hence,
(31)
{ }
1
2
2
1 1
1
0 1
1
+
=
??’
+
=
+
= =
i i i W W )] CW , ( uniform [ E
i s | TX P
8 A more formal way to derive Eq. (29) is to envision P{s=i|TX} as the steady-state probability distribution of a
discrete-time mono-dimensional Markov Chain describing the backoff stage evolution. One time step in this chain
represents a backoff stage transition, driven by the success/failure of the packet transmission. At stage 0?‰¤i
chain will evolve in the next time step in stage i+1 with probability p, and will return (or stay) in stage 0 with
probability 1-p; at stage R the chain will in any case return to stage 0 with probability 1. This interpretation allows
us to simply extend the described analysis to more general backoff processes with memory, i.
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