Considering an end-to-end scenario, if we denote the retransmission limit for each
MSDU v (transmitted via path pi) as max
i ?¤p , the average number of transmissions over path
pi until the packet is successfully transmitted, or the retransmission limit is reached, can be
calculated as:
( ) [ ] [ ] ( )[ ][ ]
[ ]
max
max
max
1
1 1 mean max max
1
1
( ) 1 ( ) 1 ( )
1 ( )
1 ( )
i
i
i i i i i i
i
i
i
j
v v v
j
v
v
t j e L e L e L
e L
e L
?¤ +
??’ ?¤+
=
?¤ +
?¤ = ?‹… ??’ + ?¤ + ?‹…
??’
=
??’
??‘p
p
p
p p p p p p
p
p
. (9)
The derivation of (9) is detailed in the appendix. The (end-to-end) expected delay for
the transmission of an MSDU of size Lv through pi under ( ) mean max
i i t ?¤ p p transmissions can be
approximated by:
( ) ( ) ( )
total total 1 1
mean max mean max
overhead queue ,
,1 1
, ()
( )
i i
i i i i i
v
v i j
i j j j
L
d L t t T d l
g l
?? ?? ??’ ??’
= =
??« ??¶??· ??¬ ?¤ = ?¤ ?‹… + +??· ??¬ ??·??·
??¬
?? ??? ??‘ ??‘ p p p p p . (10)
The last equation derives the end-to-end delay estimate by joining all links of path pi
via the summation terms, thereby forming a ???virtual??? link from the sender to the receiver
node in the multi-hop network.
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