332 H. Zhao et al.
of the M links has the same carrier sense range and hence only one link can send data at a
certain time. The service process S(0, t) of a end-to-end connection in an IEEE 802.11 DCF
channel can be obtained according to the Eq. (2)as
S
DCF
(0, t) = min
k
S
k
(t
k−1
, t
k
), k = 1, 2,...,M (3)
Although all M links can sense each other, it is worth noting that each link has a unique
service process since it contends for the channel with a unique set of neighbors. According to
[12], the e ffective capacity of a multi-hop connection, A
cm
(r) can be expressed as A
cm
(r) =
min
k
A
ck
(r),wheretheA
ck
(r) denotes the effective capacity of the link k.
When the traffic load is small with a determined service process ct,theserviceprocessofan
end to end connection in the IEEE 802.11 DCF channel [14] can be presented approximately
by using Eq. (3)as
S
DCF
(0, t) = c(t
k
− t
k−1
) =
ct
M
(4)
Through the above analysis, we know that the Eq. (4) is acquired under the condition of
a small load rate, and it is assumed that packet collisions will not happen (no data packet
retransmission). Actually, data packets are retransmitted when packet loss occurs. Therefore,
the above service process of the multi-hop connection is not suitable for the effective capacity
prediction when the load rate is high.
In response to these defects, we propose a new channel capacity prediction model which
is effective under the medium and high load rate, considering the influence caused by traffic
load rate and retransmission times of packets. The proposed algorithm not only satisfies the
statistical QoS delay requirement, but also calculates the optimal number of retransmission
times by the cross-layer QoS joint optimization in order to improve the successful delivery
rate of the wireless multimedia packets.
Since packet collision is a constant in wireless network at a high load rate, the service
process of an arrival packet can be modified as the following Eq. (5), where P
e
(·) denotes
the probability of packet collision and x is the number of retransmission times in MAC layer.
By using the packet arrival model following a Poisson distribution under any given period of
time approximately, we analyze the channel capacity prediction model based on probability
distribution.
S
DCF
∗
(0, t) = c(t
k
− t
k−1
)(1 − P
e
(x)) (5)
In wireless multi-hop Mesh networks, each link in M links can sense its neighbors. How-
ever, in order to access the service process, each link has to compete with its neighbor links,
which will inevitably lead to conflict and packet retransmission. Therefore, the calculation
of the actual channel capacity should consider the packet conflict probability and the retrans-
mission times.
We consider the case where all the L nodes belong to the single QoS index, and each
node retransmits x copies of a data packet at random instants in every interval T .Since
each node randomly and independently decides when to transmit a packet, packet arrivals
are independent of each other whether the packets are retransmitted or not. Considering the
characteristics of a wireless channel, the packet transmission duration t
f
is far less than
T . Hence the distribution of the arrival of packets to a channel within any given period of
time is approximate to follow a Poisson distribution [15] in single QoS index. As a result,
a statistical prediction model based on probability is proposed to predict the successful
delivery probability and failure probability of the packets, and we develop the capacity
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