Hence, the
guaranteed bandwidth g(li,j) of (5) can be determined for each MSDU.
Under the aforementioned assumptions for the error model of each link, the
probability of error for the transmission of MSDU v of size Lv bits is:
( ) ( ) , , 1 1 ( ) v
i j
L
l v ij e L el = ??’ ??’ . (6)
Consequently, the probability of error for the packet transmission in path pi is:
( ) ( ) ( ) ( )
total total
,
1 1
,
1 1
1 1 1 1 ()
i i
v
i ij
L
v lv ij
j j
e L e L el
?? ?? ??’ ??’
= =
??® ??? = ??’ ??’ = ??’ ??’ ??? ??? ??° ??» ??? ??? p . (7)
Notice that the derivation of (7) computes the end-to-end probability of error under the
assumption that the packet is sequentially transmitted from each link of path i.
4 We assume that one video packet is encapsulated in one MSDU and the two terms are used interchangeably.
5 For notational simplicity we do not particularly indicate the dependence of e(li,j) and g(li,j) on modulation m(li,j).
Cross-layer Optimized Video Streaming over Wireless Multi-hop Mesh Networks
111
Under a single (successful) MSDU transmission via each link li,j, the transmission delay for
path pi can be calculated as:
total 1
queue , overhead
, 1
( ,1) ( )
( )
i
i
v
v ij
i j j
L
d L d l T
g l
?? ??’
=
??« ??¶??· ??¬ = + +??· ??¬ ??·??·
??¬
?? ??? ??‘ p (8)
where dqueue(li,j) depends on the transmitting-link queue length and will be discussed in the
next subsection.
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