Outage Optimum Routing for Wireless Networks
B. Amiri, H. R. Sadjadpour
Department of Electrical Engineering
University of California, Santa Cruz 95064
Department of Computer Engineering
University of California, Santa Cruz 95064
Abstract—A new routing metric for multi-hop wireless ad hoc
networks is presented. The proposed metric is based on the
computation of Signal-to-Noise Ratio (SNR) and minimization
of wireless network outage probability in a fading environment.
This metric improves the Quality-of-Service by reducing dropped
packets. Further, by modeling the network with a Trellis diagram
and then using Viterbi Algorithm to select the best routing path,
we reduce the routing complexity of our approach. Simulation
results demonstrate the improvement achieved by implementa-
tion of this new metric. Performance of the proposed metric
is compared to other commonly used routing metrics such as
Minimum Hop Count (MinHop), Expected Transmission Count
(ETX) and two other SNR-based metrics in both mobile and
Index Terms—Mobile ad hoc networks, Routing protocols,
Outage Probability, Quality-of-Service, Signal to noise ratio,
Current high speed wireless communication networks are
used for real-time audio and video applications. For these types
of applications, connection failure is not acceptable to the end
user. Therefore, stability of wireless links is critical. For multi-
hop wireless ad hoc networks, providing route stability is even
more challenging. In these networks, link drop may result in
overall route failure. Therefore, the stability of each link in a
path can be a critical factor. In these networks, where there
are multiple paths between source and destination, finding and
selecting the most reliable path is very essential to the overall
performance of the network.
The network routing process involves two steps: first, as-
signing cost metrics to links and paths and second, distributing
the routing information in the network . Many route dis-
semination techniques ,  have been proposed to address
the second step. Proactive protocols, such as Destination Se-
quenced Distance Vector (DSDV) , and reactive protocols,
such as Dynamic Source Routing (DSR)  and Ad hoc On
Demand Distance Vector (AODV) , are proposed. Most
of these proposed routing techniques consider the number of
hops in a route called MinHop as their cost metric to find
the desired route . Although MinHop offers simplicity and
low communication delay, it may not provide a good quality
of service. In a wireless network, this metric tends to find
paths with long and unstable links which will result in lower
network capacity and reliability.
Lower stability and capacity as two critical disadvantages
of MinHop metric motivated researchers to find cost metrics
which provide better performance. These efforts resulted in
proposing new routing metrics which take into account the
quality of wireless channels –. There has been some
study to compare the performance of these routing techniques.
It is shown that none of these techniques consistently perform
better than others for different network scenarios, such as
stationary or mobile networks . The main reason for this
inconsistency is that most of these proposed routing metrics
are based on intuitive ideas rather than systematic approaches
to calculate an optimum cost metric.
In this paper, we use analytical calculation of outage
probability in wireless networks to find an optimum outage
routing metric for network reliability. This SNR-based routing
metric finds the most stable end-to-end route for wireless data
transmission. In order to reduce the routing complexity, we
model the network as a Trellis diagram and implement the
Viterbi algorithm for routing search.
Finally, we provide simulation results to verify our theoret-
ical findings. Our experiments show that our metric provides
better delivery performance compared to MinHop , ETX
, , MaxMinSNR metric proposed in ,  and the
Average SNR metric proposed in  for both stationary and
mobile network scenarios.
II. RELATED WORK
In , a routing metric (ETX) is proposed for wireless
networks based on the expected number of transmissions
(including retransmissions) necessary to transmit a packet.
Each node estimates the forward delivery ratio to each of
its neighbors and also receives the corresponding estimate
of the reverse direction. This is done by sending a probe
packet over an initialization time interval before the actual
data transmission. Then, the ETX metric is calculated based
on the inverse of these delivery ratios. It is shown that ETX
outperforms MinHop for stationary fading wireless networks
. One of the problems with ETX, though, is its perfor-
mance in mobile networks. Since probing is completed before
the actual data transmission, ETX may not be an accurate
indicator of the current channel quality  and will result
in performance deterioration in mobile networks . As
opposed to ETX, where the metric is calculated before the
real data transmission, our technique will update the routing
metric in a real time manner taking the SNR of the actual
data packets into account. Also, ETX performance in network
scenarios with multiple simultaneous flows is not as good as
in the single flow case , which is also a consequence
978-1-4244-9538-2/11/$26.00 c ⃝ 2011 IEEE
of having separate probing period for metric calculation with
lower network traffic than the actual data transmission.
In , a routing metric based on average Round Trip Time
(RTT) is proposed. In this protocol, the routing is done by
sending probe packets over each channel and measuring the
RTT of the probes. After receiving the packet, each neighbor
responds with an acknowledgment (ACK) containing a time-
stamp to calculate the RTT. RTT is designed for highly loaded
or lossy links. The major drawback of this technique is self-
interference, i.e, route instability due to load-dependence.
When a node has low load, the RTT metric for the links toward
that node is low. Therefore, more paths tend to select that
node as part of their route. This results in higher load on that
node and higher RTT metric, which leads to oscillations and
instability in route selection.
In , PktPair protocol is proposed as a modified version
of RTT protocol. This metric is based on measuring the delay
between a pair of back-to-back probes to a neighboring node.
PktPair protocol addresses some of RTT issues (mainly the
self-interference problem) but the performance is poor as a
result of high overhead. In , the performance of ETX ,
RTT , PktPair  and MinHop are compared. It is shown
that ETX has the best performance in a stationary wireless
network while MinHop demonstrates a better performance
than ETX in mobile cases. Considering these results, we only
select ETX and MinHop among the above four metrics as part
of our performance baseline for simulations.
In addition to the above mentioned metrics, there are some
other proposed routing metrics based on SNR. Incorporating
SNR calculations in the routing metric derivation is a promis-
ing approach, as it addresses the difficulty of defining good and
bad links in wireless networks. Thus, there are many separate
levels of link quality that can be expressed by the SNR. In
, a routing strategy is proposed to find the most stable path
in the network, the one with the minimum end-to-end outage
probability. It is assumed that the bottleneck link, i.e., the link
with the minimum SNR, limits the throughput of a path and
an outage can happen only due to a drop in this bottleneck
link. The main drawback of their strategy is that the derived
metric is not composable, i.e., it does not take into account
the performance of all links in the path but only the weakest
one. Nevertheless, failures can also happen in other links.
This is more likely when there are multiple links in a path
with SNR close to the minimum SNR.“Being composable”
is an important property of a routing metric so that the end-
to-end path cost can be easily derived from the individual
link metrics along the path. The metric we propose in this
paper is a composable metric (similar to ETX and RTT) and
takes into account the performance of all links to determine
path performance. Our simulation results demonstrate that this
strategy provides performance improvement compared to other
In , a very similar approach to  is proposed. In this
paper, traditional DSR routing technique is modified so that
the source node selects the route based on the value of the
best of the worst link SNR and Received Power (RP) among
all possible routes. The general performance of this proposed
technique is expected to be similar to .
In , MinHop and link quality are considered sequen-
tially. First, the path(s) with the minimum number of hops
are extracted. If more than one path is found, then the path
with stronger links, in terms of average SNR, is selected. If the
number of hops is different, no SNR calculations are made and
the path with MinHop will be selected. On the contrary, our
new metric allows comparison of multiple paths with different
number of hops, thus, it is more general and can achieve higher
The outage probability model for a network that suffers
from fading was also exploited in . The authors developed
a probabilistic model and studied the relationship between
link reliability, distance between nodes and the transmission
power. Algorithms to find the optimal link were developed by
taking advantage of route diversity. The emphasis of this work
was on the trade-off between reliability and end-to-end power
consumption, whereas we focus on the computation of the best
path with minimum outage probability.
III. METRIC DERIVATION
This paper considers maximizing path reliability as the main
criterion in route selection for wireless ad hoc networks and
our goal is to find a routing cost metric to minimize the outage
probability. In addition, a good routing metric for practical
applications should be simple and composable.
We first start by calculating the link outage probability. In a
Rayleigh fading environment, the channel gain can be modeled
as a complex Gaussian random variable with zero mean and
two Gaussian random variables X and Y , Z =
and Z2are Rayleigh and exponentially distributed respectively.
The transmit power is and the received signal power will be
exponentially distributed with mean σ2
white Gaussian noise with variance N0/2 per complex dimen-
sion is added to the received signal. With a finite bandwidth
of B Hz and transmit power of PT, the average received SNR,
¯ γm, including path loss and shadowing is
mper complex dimension . Note that for any
m. Further, an additive
¯ γm= σ2
The outage probability of link m in path i can be calculated
m< γth) = 1 − P(γi
where γth is the SNR threshold required to support system
desired data rate. For an exponentially distributed received
SNR, this probability is given by
out,m= 1 − exp(−γth
Eq. (3) shows link outage probability as a function of SNR.
The next step is to calculate path outage probability. Assum-
ing link independence in a path, outage probability of path i
with Mihops is given by
out,m) = 1−exp
ln(1 − Pi
The path with optimal outage, iopt, can be computed as
Replacing link outage probability from Eq. (3) into Eq. (4),
we arrive at
1 − exp
ln(1 − Pi
ln(1 − Pi
−ln(1 − Pi
Note γthis fixed for all links and can be eliminated from this
Eq. (6) suggests that the path metric is equivalent to the
summation of inverse SNR of all the links in the path. This
metric finds the outage optimum path and has two important
properties of a good routing metric. It is simple and compos-
able. By calculating the inverse SNR metric for all possible
paths from source to destination and finding the path with
minimum cost metric, we can find the most stable and reliable
path, i.e., the one with the minimum outage probability.
It is important to mention that the authors in  have used
outage probability model to find cost metric with the general
assumption that path outage only happens as a result of outage
in the weakest link of the path. This assumption has resulted
in a different routing metric which is not optimal and is not
composable. We call this metric MaxMinSNR in this paper.
We provide an example to better illustrate the difference be-
tween the Inverse SNR metric proposed in this paper, MinHop
metric used in – and MaxMinSNR metric proposed in
 and . Figure 1 illustrates a simple network scenario.
There are six nodes: one source (S), one destination (D) and
four intermediate nodes. The SNR of each link is shown by
a number next to it. There are three different possible routes
from source to destination. Route 1 (S-N1-N2-D) and Route
3 (S-N4-N3-D) have three hops while Route 2 (S-N3-D) has
two hops. Therefore, MinHop routing will select Route 2 as the
best route without taking link SNR into account. MaxMinSNR
considers the minimum SNR of each path and will select the
route with the highest minimum SNR. Therefore MaxMinSNR
will select Route 3 as the best route.
In the case of Inverse SNR routing presented in this paper,
the metric for each route is the summation of inverse SNR of
all the links in that route. By simply adding link metrics, the
route metric for Routes 1, 2, and 3 are equal to 0.2667, 0.3175
and 0.4420 respectively. Therefore, Inverse SNR routing will
select Route 1 as the best route.
This simple example shows how each of the SNR-based
routing metrics may select a completely different route. In the
simulation section, we will provide the results and compare
the performance of these routing metrics.
Fig. 1. A simple example with three possible paths from source to destination
IV. A FRAMEWORK FOR ROUTING SEARCH
Calculating link and path metrics to find the best route
from source to destination among all possible routes can be a
very complex task in large networks. Therefore, simplicity of
routing protocols is very important. In this section, we propose
a general framework for mapping the Viterbi algorithm to
routing search protocols.
The first step is to model a multi-hop wireless network with
a Trellis diagram. A Trellis diagram is a finite state machine
which is constructed by states, branches and stages. In a Trellis
diagram, there are finite stages from the Trellis starting point
to its end point. Also, there are finite states at each stage. We
consider a Trellis diagram with M stages and N states at each
step (Fig. 2). Each branch which starts at state x in stage m
and ends at state y in stage m + 1, has a determined weight
(where x and y are less than N). There are several paths from
the Trellis start point to its end point and each path consists
of M states and branches. The path weight is composable of
its branch weights. As a result, each path has an associated
weight and the path with minimum weight will be selected as
the final solution.
The idea is to model a network as a Trellis diagram. A multi-
hop network has a finite number of hops and intermediate
nodes which we call relay. Assuming a network with a
maximum of M hops and N relays at each hop, each link
from node x at hop m to node y at hop m + 1 has a cost
metric (both x and y are less than N) which is an indicator of
the performance and quality of that link. Path metrics can be
calculated from link metrics.
With this general modeling, the Trellis start- and end- points
can be mapped to source and destination nodes in a network
and the number of stages in a Trellis diagram can be mapped
Fig. 2.4-state Trellis Diagram
to the number of hops in a network. Each state in Trellis will
be similar to a node in the network and the number of states
will be equivalent to the maximum node degree in the network.
Branch weight in a Trellis is similar to link metric in network
routing and the goal in both Trellis and routing is to find the
path with minimum cost metric.
Viterbi algorithm is a dynamic programming approach used
to run an optimal sequential Trellis search to minimize the
error by finding the most likely sequence of states. As it is
illustrated above, a Trellis diagram model can be implemented
for a network. Since both Viterbi algorithm and network
routing are dynamic programming approaches, the next step
will be to show how running Viterbi algorithm for a Trellis
diagram is similar to finding the best possible route from
source to destination in a network. A more comprehensive
modeling will be done in future works.
Viterbi algorithm will perform a full search while minimiz-
ing the complexity by dynamically eliminating sub-paths with
lower performance originating and ending at common nodes.
The Viterbi algorithm implementation will help reduce the
complexity of the full Trellis search while keeping the optimal
performance. This means that we can reduce the complexity
without any performance degradation. More significantly, this
mapping framework can be used as an initial step to implement
other (already existing) suboptimal Trellis search algorithms
with lower complexity into the network routing concept.
It is important to mention that the work presented in this
section is only the initial step of a general framework. More
details on this framework and other suboptimal schemes are
required for a more comprehensive modeling which is beyond
the scope of this paper and will be presented in future works.
In this section, we will first explain details of the simulation
environment. Then, we will present simulation results for the
Inverse SNR metric introduced in this paper and compare them
to other techniques.
A. Simulation Environment
We use Qualnet  as the simulation environment for our
experiments. We randomly distribute 30 nodes in a 1000m ×
1000m square area with Rayleigh fading. For the stationary
scenario, nodes are fixed and for the mobility scenario each
node has a random speed of 1–10 m/s. This scenario mimics
an environment where people walk, run or ride bicycle.
Each node runs IEEE 802.11 as the MAC protocol and
802.11b as PHY model with a transmit power of 15 dBm.
For each measurement, two nodes are randomly selected as
source and destination. Constant-Bit-Rate (CBR) traffic is used
to simulate the performance of generic multimedia traffic.
This UDP-based, client-server application sends data at a
constant bit rate. The source node transmits 50000 packets
of size 2048 bits with 500 packets/sec CBR. The number
of received packets is measured to calculate delivery ratio.
Thirty measurements are done with different random pair of
source and destination nodes and averaged to represent the
performance of each technique.
B. Simulation Results
We modified the reactive DSR routing protocol  to
implement the Inverse SNR metric. When a source S is
interested in a destination D, the route is set up on-demand
by sending a Mesh Request (MR). The MR is replied by a
Mesh Acknowledgment (MA) from the destination D, which
is re-broadcasted by intermediate nodes toward the source. To
implement the Inverse SNR metric into DSR, a weight label
is defined for each route. Whenever a packet is received by
an intermediate node, the SNR of the packet is calculated.
Then the intermediate node adds the inverse of link SNR
to the weight label received from the upstream neighbor to
update the weight label. Therefore, the overall route weight
label is composable by adding link weight labels. This process
continues until we reach the source node S. The source node
receives weight labels from all routes and selects the route
with the lowest weight label (route metric).
Since link SNR can rapidly change in a mobile wireless
environment, exponential moving average is used for SNR
measurement smoothing as
SNRt= α × SNRt−1+ (1 − α) × SNRins.
SNRt and SNRt−1 are the new and old smoothed SNR
respectively and SNRinsis the current (instantaneous) SNR
value. Smaller α value gives more weight to the current
measured SNR, whereas larger values give more weight to the
previous average measurement. Having a small α may result
in rapid change in the average SNR and frequent switching of
the selected path, which is undesirable for the stability of the
system. On the other hand, a large α value may result in some
undesirable delay in route switching when the quality of the
route deteriorates. Therefore, optimization of α value can be
a determining factor in the performance. For our simulation,
α = 0.9 is used for different network scenarios.
Results are presented in terms of the number of delivered
packets and average end-to-end delay. Number of delivered
packets is a good metric for system stability performance.
Since the transmission data rate and the total number of
transmitted packets are fixed (CBR), the number of delivered
packets is also a representative of the throughput.
End-to-end delay is the one-way delay between the time
that source sends the packet and the time that destination
receives it. It is averaged over all received packets. For
CBR transmission, delay can be due to the network layer
queue, MAC layer delay, transmission delay and propagation
delay . The propagation delay depends on the distance
between nodes in a wireless network, and the transmission
delay depends on the link bandwidth. Therefore, analyzing
end-to-end delay will be more complicated than the number of
delivered packets since the former is dependent on the route’s
physical length, bandwidth and other network parameters.
We have conducted simulation results for two well-
established routing metrics, MinHop  and ETX  , as
well as two recently proposed metrics, MaxMinSNR  
and Average SNR , all of which implemented for the DSR
routing protocol. The DSR implementation of ETX is done as
explained in  and the DSR implementation of MaxMinSNR
and Average SNR is done similar to the process explained
in . The following text explains details of stationary and
mobile simulation scenarios.
1) Stationary network: In this section, we evaluate a sta-
tionary network scenario where all 30 nodes are fixed during
the simulation. For each metric, the simulation is done for 50
random node pairs and results are averaged and displayed. We
provide and compare the average number of delivered packets
and average end-to-end delay as performance indicators for all
five above mentioned metrics.
As it is shown in Fig. 3, Inverse SNR has the highest
and MinHop has the lowest average packet delivery ratio.
Average-SNR technique shows improvement compared to Min-
Hop, which is consistent with the results in , but the
improvement is only less than 5 percent. The reason for this
minor improvement is that Average SNR modifies the route
only when there are multiple routes with the same number
of hops which is not applicable to all scenarios. MaxMinSNR
shows better performance compared to MinHop which is also
consistent with  but still has a lower delivery performance
compared to ETX and Inverse SNR. As it is shown here and
previously in , ETX performs well in stationary networks,
however Inverse SNR continues to be superior. This is in
line with our analytical work where it is demonstrated that
Inverse SNR minimizes the outage path probability resulting
in maximized delivery performance.
The average end-to-end delay comparison is shown in Fig.
4. As explained before end-to-end delay can occur as a result
of network layer queue, MAC layer delay, transmission delay
and propagation delay. Therefore, analyzing details of end-
to-end delay for all five techniques is complicated, but our
simulation results shows the superiority of the Inverse SNR
metric. Also as it is shown, MinHop demonstrates fairly good
delay performance compared to other techniques which could
be attributed to a lower propagation delay compared to other
2) Mobile Network: We have also conducted simulations
for the mobile scenario where nodes are moving with random
mobility of 1–10 m/s. This case can be a representative of
Inverse SNR delivers more packets on average than all the other
Fig. 4.Inverse SNR has smaller average delay than all the other metrics
the scenario when people are roaming while holding wireless
transceiver enabled devices in an office environment.
The average delivery performance for all five metrics is
presented in Fig. 5. Similar to the stationary cases, Inverse
SNR provides better stability (delivery ratio) and throughput
performance. ETX has the worst performance compared to
others because it allocates an initial probing time before the
actual data transmission for link metric calculation. By the
time of actual data transmission, the metrics calculated during
probing may change resulting in an inaccurate evaluation of
the link performance. Therefore, ETX only provides perfor-
mance improvement for stationary cases which is consistent
to findings in .
Average end-to-end delay comparison for mobile cases is
shown in Fig. 6. For this scenario, MinHop and Average SNR
provide slightly better performance of 6 and 4 percent respec-
tively compared to Inverse SNR while ETX and MaxMinSNR
have the highest average end-to-end delay. Similar to the
Fig. 5. Inverse SNR has the highest throughput in a mobile scenario
stationary case, analysis of end-to-end delay for all five tech-
niques is complicated because it depends on many different
Fig. 6. End-to-End Delay Comparison of all metrics mobile environment
Given the superior performance of this technique for station-
ary networks and better packet delivery for mobile scenarios,
this approach is particularly suitable for applications that are
sensitive to packet losses. Note that the delay of this technique
is very close to the best techniques in our simulations.
This paper introduces a new routing metric based on the
inverse SNR criterion for wireless networks. This metric
is derived by theoretical calculations to minimize the path
outage probability in a wireless network and maximize the
network delivery performance in fading environments. Sim-
ulation results show that this Inverse SNR metric has better
delivery performance compared to MaxMinSNR, Minhop, Av-
erage SNR and ETX routing in both mobile and stationary
wireless networks. Further, the Inverse SNR scheme is a
composable metric which is desirable for path selection. We
also demonstrated how to take advantage of Viterbi algorithm
to implement Inverse SNR approach.
This research was partially sponsored by the U.S. Army
Research Laboratory under the Network Science Collabora-
tive Technology Alliance, Agreement Number W911NF-09-
0053, by the Army Research Office under agreement number
W911NF-05-1-0246, by the National Science Foundation un-
der grant CCF-0729230, and by the Baskin Chair of Computer
Engineering. The views and conclusions contained in this
document are those of the author(s) and should not be inter-
preted as representing the official policies, either expressed
or implied, of the U.S. Army Research Laboratory or the
U.S. Government. The U.S. Government is authorized to
reproduce and distribute reprints for Government purposes
notwithstanding any copyright notation hereon.
 E. Hossain, K. Leung, Wireless Mesh Networks: Architectures and Pro-
tocols, Springer Science, New York, 2007, pp. 227–242.
 E.M. Royer and C.-K. Toh, A review of current routing protocols for Ad
Hoc mobile wireless networks, IEEE Personal Communications, April
1999, pp. 46–55.
 M. Abolhasan T. Wysocki and E. Dutkiewicz, A review of routing
protocols for mobile ad hoc networks, Ad Hoc Networks 2, Jan. 2004,
 C.E. Perkins and P. Bhagwat, Highly dynamic destination sequenced
distance-vector routing (DSDV) for mobile computers, Wireless Personal
Communications, Feb. 1997, pp. 36–45.
 D.B. Johnson and D.A. Matlz, Dynamic source routing in ad hoc wireless
networks, Mobile Computing, 1996, pp. 153–181.
 C.E. Perkins and E.M. Royer, Ad-hoc on-demand distance vector routing,
Proceedings of the Second IEEE workshop on Mobile Computer Systems
and Applications, Feb. 1999, pp. 90–100.
 D. Couto, D. Aguayo, J. Bicket and R. Morris, A high-throughput
path metric for multi-hop wireless routing, ACM Conference on Mobile
Computing and Networking (MOBICOM), Sep. 2003, pp. 134–146.
 C.E. Koksal and H. Balakrishnan, Quality-aware routing metrics for
time-varying wireless mesh networks, IEEE Journal on Selected Areas
in Communications, Nov. 2006, pp. 1984–1994.
 B. Gui, L. Dai and L.J. Cimini, Jr., Routing strategies in multihop
cooperative networks, IEEE Transactions on Wireless Communications,
Feb. 2009, pp. 843–855.
 A. Adya, P. Bahl, J. Padhye, A. Wolman, and L. Zhou, A multi-radio
unification protocol for IEEE 802.11 wireless networks, Technical Report
MSR-TR-2003-44, Microsoft Research, July 2003.
 R. Draves, J. Padhye and B. Zill, Routing in multi-radio, multi-hop
wireless mesh networks, ACM Conference on Mobile Computing and
Networking (MOBICOM), Sep. 2004, pp. 114–128.
 R. Draves, J. Padhye, and B. Zill, Comparison of routing metrics for
static multi-hop wireless networks, ACM conference of Special Interest
Group on Data Communication (SIGCOMM), Aug. 2004, pp. 133–144.
 F. Alnajjar and Y. Chen, SNR/RP Aware Routing Algorithm: Cross-
Layer Design for MANETs, International Journal of Wireless and Mobile
Networks (IJWMN), Nov. 2009, pp. 127-136.
 Y. Zhou, S. Chung, L. Yang and H. Choi, A link-quality aware routing
metric for multi-hop wireless network, International Conference on Com-
munication Software and Networks (ICCSN), Feb. 2009, pp. 390–394.
 A.E. Khandani, J. Abounadi, E. Modiano and L. Zhang, Reliability and
Route Diversity in Wireless Networks, IEEE Transactions on Wireless
Communications, Dec. 2008, pp. 4772–4776.
 D. DeCouto, High-throughput routing for multi-hop wireless networks,
Ph.D. thesis, Massachusetts Institute of Technology, June 2004.
 X. Ni, K. Lan and R. Malaney, On the performance of expected
transmission count (ETX) for wireless mesh networks, Workshop on
Modelling and Design of Wireless Mesh Networks (MODENETs), Oct.
 A. Goldsmith, Wireless Communications, Cambridge University Press,
New York, 2005, pp. 69–72.
 TheQualnet simulator,Scalable