wireless networks. According to ITU-T J.241, an
input value of T
must be less than hundreds of
milliseconds and a jitter less than tenths of
milliseconds in order to be tolerated for high quality
video streaming services. Video packet-loss rate
(P
) refers to end-to-end video packet-loss rate and
should be less than 10 %.
ITU-T G.1070 provides an algorithm that
estimates video quality. According to the ITU-T
G.1070, objective measurement of video quality, V
,
is calculated by:
=1+
−
(1)
where D
is degree of video quality robustness
due to packet loss; P
is video packet-loss rate;
I
represents the basic video quality affected by
the coding distortion under a combination of video
bit rate and video frame rate. I
is objective
measurement of basic video quality accounting for
coding distortion.
Every video content has its own video quality
robustness D
, and its own objective
measurement of basic video quality accounting for
coding distortion, I
. These two values are able
to be derived by applying the method described in
ITU-T G.1070. We only cite some measurement
from (You, 2009), and list them in Table 1(To
simply discussion, we assume D
is constant
under different P
and I
is constant with
different video bit rate and video frame rate). Thus,
in this paper, we only focus on how to obtain video
packet-loss rate, P
, using Markov chain analytical
model (Bianchi, 2000).
Table 1: Coefficients of I
coding
and D
PplV
for a video.
value 3.655 0.0037
2.2 Analysis Model under Saturation
Condition
We use the two-dimensional saturation Markov
chain models shown in Figure 1 to analyze the
packet dropping rate of IEEE 802.11. In the analysis,
we assume that the wireless networks operate in an
ideal physical environment, being the same one in
Bianchi’s model (Bianchi, 2000).
In the discrete-time Markov Chain shown in Figure
1, we define b
,
as the stationary distribution
probability of being in state (j,k), where j∈
0,L
)
is
the backoff stage, k∈0,w
−1 is the backoff
counter and w
is the contention window size at
backoff stage j.
Define m as maximum backoff stage when
contention windows will double. By the Markov
Chain regularities, a normalization requirement,
1=
∑∑
b
,
+
∑
b
,,
, and w
=
2
w
j≤m
2
w
m< ≤
,
we obtain
1
b
,
=
1−2p
2
1−p
)
−
p−p
2
1−p
)
1−p
)
+
w
2
1−p
)
1+
2p −
2p
)
1−2p
)
+
2
p
−p
)
1−p
(2)
where p is a probability that a node senses the
channel busy in a random slot. We denote τ the
transmission probability that a node attempts to
transmit a packet in a randomly chosen slot time.
Knowing that any transmission occurs when the
backoff time counter equals to zero, we will have
Equation (3).
τ=
b
,
=
1−p
1−p
×b
,
(3)
Substituting equation (2) into equation (3)
furthermore, we obtain equation (4) for the node’s
transmission probability τ.
τ=
)
)
)
)
)
)
)
(4)
Equations (4) are called the IEEE 802.11 node
property formula since it represents a binary
exponential backoff scheme to access to the
medium. It determines the node's transmission
probability in terms of the channel busy probability
as well as the network configuration parameters
(L,m,w
). The set of variables of
p,τ
in equation
(4) will be regarded as the attributes of a
transmission of an IEEE 802.11-based station with
arbitrary traffic arrival rate. Noticing that every node
i will have its own
p,τ
, we now attach the node’s
serial number to
p,τ
and formulae (4) become
equation (5), where i=1,2,… N; and N is number of
nodes in the network.
(5)
τ
=If the packet has not been successfully
transmitted after packet retry limit L times
attempting, the packet is dropped. Hence, the packet
dropping probability can be estimated as: p
=
p
(collision L+1 times before dropping). If the
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