1. On Routing Metrics in Wireless Mesh Networks
Nejat Onay Erkose (PhD. Candidate), Ranil Santhish Gamage (MSc.)
Institut national des Télécommunications
I. INTRODUCTION
Finding the best paths in any type of network has always
been a challenging problem for the researchers. What makes
finding the best paths so difficult is a relative question whose
answer can be found by looking at the kind of network type
and its topology under study. While studying the question in
wired networks is not a big challenge, approaches to this
question may be highly sophisticated in ad-hoc networks and
the newly emerging networking scheme wireless mesh
networks on which we will orient our discussion.
Wireless Mesh Networks is conceived to offer broadband
wireless access to the internet. The nodes in Wireless Mesh
Networks automatically discover each other and maintain
connectivity. The auto-forming nature of WMNs facilitates its
deployment and usage in cases where wired infrastructure is
not possible or expensive.
The backbone of a mesh network is formed by Mesh Points
(MPs). According to their functionality there are different
types of MPs. Some of the MPs depending on their
capabilities can provide network connection for legacy devices
(i.e.Mobile computers, PDAs, and other devices which can
benefit from MAP services). This type of mesh point is called
a MAP (i.e. mesh access point) and it functions both in
infrastructure and ad-hoc modes. A non-AP mesh point helps
providing mesh services to the other MPs and forms the
backbone of the WMNs with MAPs. A third type of MP is
called a lightweight Mesh Point. Congestion control and
distribution system services (DS) are not offered by this type
of MPs, but they can still provide the services common to all
other non-AP mesh points [14]. Besides these types there is
one more type of node in the mesh composition. This type,
however, has non-mesh point characteristics with ability to
benefit from the advantages that are provided by a mesh
network, namely, devices (i.e. Mobile computers, PDAs, and
other devices) that can get network access through MAPs.
An interesting point is while MAPs are definitely static
nodes in the network, some of the MPs can be mobile, and
therefore any routing protocol, so as any metric must be
carefully designed or used, by taking this WMNs-special
characteristic into account.
Apparently, one of the operations that a routing protocol
must undertake is to make various measurements to be able to
find out the best path or paths between two nodes in a
network. Many different types of measurements can be
undertaken based on some physical phenomena (i.e. load on
the link, congestion, node energy level, interference on the
channel etc…). In routing terminology, the criterion to
evaluate a path’s “goodness”, obtained by these measurements
is called a routing metric.
Depending on the requirements of the specific network
technology that is under study, some measurements may be
more preferable over others. For example, parameters we
might like to measure and design for path estimation in ad-hoc
networks maybe different than static multi-hop networks. In
our case, in WMNs, the requirements to design routing metrics
are subtly different than those in wired and ad-hoc networks.
This difference is emerging from the hybrid mobility scheme
that WMNs posses (mobile MPs and static MAPs) and multi
channel/radio usage on nodes. First, in WMNs not all the
nodes, in contrast to the assumption in Yang et al.’s work [1],
are static, neither most of them are mobile but composed of
mostly static and many mobile mesh nodes which take role in
routing decisions [14]. The second difference is the multi
channel/radio nature of WMNs. While this feature, on one
hand, facilitates the communication between nodes, it adds up,
on the other hand, to the complexity of path finding and
evaluation due to the new measurement criterion. Therefore, a
routing metric should be conceived in the most appropriate
ways to conform to the characteristics of the WMNs, in order
to get the highest network performance.
Many different approaches, based-on the information
extracted from different layers, have been undertaken in
metric design. The on going researches show that this kind of
cross-layer design approach is indispensable for a routing
protocol to improve the performance of the network [3], [5],
[6]. Hence, we will mostly focus our discussion on the metrics
formed by using lower layer (PHY and Link layer)
information to be used in the network layer.
In order to bring some insight to our report we are going to
analyse and discuss some of the metrics that are so far created.
Among them we will have a look at hop count [15], RTT [15],
PktPair [15], ETX [16], ETT,WCETT [17], MIC [1], FTE [6],
PSR [5], “WMNs draft” metric [14], mETX,ENT [4]. We will
also present a summary of energy-based routing aspects.
The following is the structure how this report is organized:
In the first section we will have a look at the design goals for a
good routing metric, and study pros and cons of the above
mentioned metrics. In the third chapter, we will present some
aspects of routing in WMNs. The ensuing section is a brief
discussion of studied metrics and our future direction of.
Finally, in section five, we will conclude the report.
II. A COLLECTION OF ROUTING METRICS
A. Network Performance Based Metrics
According to Yang et al.[1], there are four requirements in
design of routing metrics. These are route stability, good
performance for minimum weight paths, efficient algorithms to
calculate minimum weight paths and loop-free routing.
The first requirement necessitates the stability of the path
weights. Since if we have paths with constantly changing

2. weights the routing metrics will have to recalculate all the
routes each time a path weight change occurs. This is so,
especially in load-sensitive metrics since it the link load is
prone to change with incoming and outgoing of each flow.
Topology-dependent metrics, on the other hand, are more
stable since weights take their values from link properties such
as number of hopes to the destination or capacity of the links
on a route.
The second requirement, good performance for minimum
weight paths, says simply that a metric should find the
minimum sum of link costs between a source and a
destination. Moreover, Yang argues that achieving this goal
depends on how good a metric can conform to properties of a
specific kind of network characteristics. In the case of Mesh
networks, they identify these characteristic properties (which
are valid for ad-hoc networks as well) as path length, link
capacity, packet loss ratios, and interference.
The third requirement, efficiency of algorithms to calculate
the path, is rather a property of a routing protocol than a
metric. Yang et al. in their work, relate this to a property
called isotonicity which is necessary and sufficient condition
for routing algorithms( Djikstra’s and Bellman) to calculate
paths in the most efficient and accurate way[1]. Isotonicity
simply means that if a path’s weight from a node A to a
destination node B (see the below figure) has a cost of C1 and
another path’s weight between same pair has a cost of C2,
where C1 ≤ C2, then the cost weight relationship from node A
via node B to a node C, where B-C path cost is C3, should not
be other than C1+C3 ≤ C2+C3.
Figure 1. Isotonicity Property [1]
The last requirement is identified as loop-free routing. In
their work, since they consider hop-by-hop routing as the most
suitable routing scheme for wireless mesh networks, and for
this scheme to work loop-free with Djikstra’s algorithm, the
metric has to be isotonic. In other routing schemes such as
source routing, on demand routing or distance vector routing,
in contrast, isotonicity is not a requirement.
Many other articles have mentioned more or less similar
requirements [15][16], mainly based on link loss ratios, their
variability [4], end-to-end throughput, asymmetric link loss
ratios, signal strength, transmission rates, bandwidth usage
and interference.
We will further our study with a close look to some of these
metrics and their pros and cons.
a) Hop Count
The most commonly used routing metrics by many
protocols such as DSR[11], DSDV[9], AODV[10]. The
performance criterion for hop count is the length of the path to
the destination. Although its usage is widespread, it lags
behind many important aspects that are indispensable
especially for wireless networks. Among these points,
interference, loss ratios, channel variability, transmission rates
or bandwidth are not taken into account by this metric. Thus, it
does not provide the optimum means of path calculation for
routing protocols.
B) Per-hop Round Trip Time (RTT)
This is a well know metric in wired networks. The basic
idea of this scheme is based on sending small size unicast
packets with timestamps to each neighbour, at each 500ms.
Each neighbour sends acknowledgements to the sender node,
echoing the timestamp. The sender node processes these
packets to calculate the delay by comparing the current time
against the timestamp value on the ACK packet. Sender node
keeps an exponentially weighted moving average of these
values and increases the average by 20% if these small size
measurement packets are lost. The same kind of penalty is
applied if any data packet is lost during further
communication.
RTT’s design goal is to avoid heavy load links, therefore it
is a load-dependent metric. This scheme also takes into
account different parts of link quality aspects such as queuing
delays, busyness and contention on a channel as well as
channel loss ratios. For example, if neighbour node is busy
queuing delays have a great effect on the RTT. Similar impact
will be observed, if the nodes around the sender are
contending for the same channel or if the link is lossy.
As in the hop count scheme, interference, data rates,
channel variability are not included in the design of this
metric. One of the other disadvantages of RTT is self-
interference which can be best explained as competition for
channel access between nodes on the path of the same flow.
Another one is that the overhead imposed by each node by
sending estimation packets to every other node.
Since RTT it is a load-dependent metric, it less preferable
for dense networks because load-dependency causes to route-
instability and therefore recalculation of paths each time the
link weight changes which will cause a considerable delay in
network layer.
c) Per-hop Packet Pair Delay (PktPair)
The design goal for PktPair is to fill some of the gaps that
RTT lagged behind. Therefore, PktPair is based on a similar
mechanism to the RTT. In this scheme the sender node sends
two back-to-back estimation packets each two seconds. The
first of these packets is a small one while the second one is a
larger packet. Delay between these two packets are calculated
by the receiving node and communicated back to the sender
where the exponential moving average of these values is kept.
The part left out for the routing algorithm is to minimize the
sum of these delays.
C2
C1
A B
A
C1
C2
C3
B
C
C
C3 C1
C2B
A

3. In addition to the link quality aspects that are taken into
consideration by RTT, PktPair metric accounts for bandwidth
by sending a larger packet. For example, if the link between
the node and its neighbour has a low bandwidth, the second
packet will take more time to be delivered. Moreover PktPair
is immune to queuing delays in the sender node since all the
packets are equally delayed.
One big disadvantage of PktPair is that the overhead exerted
to the network by estimation packets is huge due to two
packets. Similar to RTT, PktPair is not immune to self-
interference [16].
d) Expected Number of Transmissions (ETX)
DeCouto et al. [15] define ETX of a link as the predicted
number of MAC layer data transmissions and retransmissions
to deliver a packet successfully over that link. Accordingly,
the ETX of a route is the sum of all the links ETXs on the
path.
As proposed by DeCouto et al., ETX estimates the number
of retransmissions required to send unicast packets between
two wireless neighbouring nodes. This is achieved by each
node broadcasting small link probes (134 byte) thereby
measuring the delivery ratio of broadcast packets. Each node
broadcasts a probe packet once per second containing the
count of probes received from each neighbouring node in the
previous 10 seconds. The counts obtained from broadcast
probes avail the sender to estimate the number of
retransmissions in unicast packets.1
Once the link metrics are
found the path metric corresponding to a particular route could
be calculated as the sum of the ETX values for each link in the
path.
The mechanism of ETX relies on reverse and forward loss
probability measurements on a link. To start with, the
probability that a packet transmission is not successful, p, is
derived by using forward and reverse loss probabilities, df and
dr respectively.
)1(*)1(1 rf ddp −−−= (1)
Since MAC layer will retransmit the unsuccessful attempts
of packet transmissions, the probability of having success after
“k” attempts, s(k), has to be calculated:
)1(*)( 1
ppks k
−= −
(2)
Thus, ETX will be:
p
kskETX
k −
== ∑
∞
= 1
1
)(*
1
(3)
ETX predicts throughput for short routes (i.e. Link
throughput ≈ 1/ Link ETX) and quantifies loss, asymmetry
and throughput reduction of longer routes [15].Since both long
1
IEEE 802.11 link layer retransmissions and acknowledgments were
assumed and 802.11 ARQ mechanism retransmit packets if either data or
acknowledgement is lost
paths and lossy paths have large weights under this metric, it
captures the effects of both path loss ratios and path length.
As a performance comparison, ETX metric outperforms hop
count metric even though it uses longer paths. The probing
overhead is substantially reduced as a result of broadcast
probe packets being used instead of unicasting them.
ETX has several disadvantages:
• Its estimates are based on measurements of a single
link probe size of 134 bytes. Hence it underestimates
data loss ratios and overestimates acknowledgement
loss ratios.
• The metric does not directly account for the data rate.
• ETX does not perform well in environments with
multiple radios and channel diversity [15].
• Time varying wireless channel conditions (e.g.
channel having low packet loss ratios, but with high
variability) are not taken into account [4].
• Interference issue is not addressed.
e) Expected Transmission Time (ETT)
ETT is an improvement over ETX which takes the different
link transmission rates into account. ETT is the expected link
layer duration for a successful transmission of a packet at
particular link.
ETT = ETX
B
S
× (4)
Where B is the transmission rate (bandwidth) of the link and S
is the packet size.
Even though this metric considers the transmission rate in
calculating path metric, it inherits other weaknesses of ETX.
In particular, ETT does not fully capture the intra/inter-flow
interference in the network. For example, it may choose a path
that only uses a single channel, even though a path with
diversified channel can exist which has less intra-flow
interference thereby higher throughput [1].
f) Weighted Cumulative ETT (WCETT)
WCETT was proposed by [17] introducing an additional
property to the sum of ETTs. The newly added property
favours paths that are more channel-diverse. This property
describes the bottleneck channel along a particular path. In
addition, WCETT succeeds to capture the self-interference by
taking into consideration the number of nodes using the same
channel along the path.
If there are n hops on a k-channel system:
Xj = ∑=
n
i
i
1
ETT 1 < j < k (5)
The above equation can be interpreted as the sum of ETTs of
links, from a source to a destination, that are on channel “j”.
WCETT= (1-β) ∑=
n
i
i
1
ETT + β X j
kj<≤1
max (6)

4. Two properties are considered in the process of designing
WCETT. Increasing nature of the path metric (as more links
are added) is represented by ∑=
n
i
i
1
ETT , while X j
kj<≤1
max
favors the paths that are more channel diverse. A tunable
parameter β (0 =<β =<1) combines these two desirable
properties by providing weights. WCETT can be considered as
a metric that balances the choice between delay and
throughput described by the first and second terms
respectively.
While fulfilling many other requirements of metric design,
WCETT does not consider channel variability on links and
inter-flow interference. The later notion is the fact that a flow
on a wireless path will use the bandwidth of the links on its
path, while contending for the bandwidths of neighbouring
links. WCETT, in addition, is designed to be deployed in
environments where more than one channel is supposed to be
used.
g) Metric of Interference and Channel – switching (MIC)
As WCETT, the MIC is a ETT-based metric and improves
the WCETT by introducing a mechanism that can solve inter-
flow interference.
MIC is composed of two parts IRU (interference-aware
resource usage) and CSC (channel switching cost). With IRU,
MIC attempts to capture the inter-flow interference whereas
CSC is conceived to control intra-flow interference (see eq.7).
IRU and CSC are defined in [2] as:
lll NETTIRU *=
Nl is interfering set of neighbour nodes in the vicinity of link l.
=iCSC {
))()((
))()((
2
1
iCHiprevifCHw
iCHiprevifCHw
=
≠
}
0 ≤w1<w2
CH (i) represents the channel assigned for node i’s
transmission and prev(i) represents the previous hop of node i
along the path p. The above statement implies that any two
consecutive links using the same channel will be penalized
with a higher link cost value in order to reduce intra-flow
interference thereby favouring paths with more diversified
channels.
IRU represents the total amount of channel time - belonging
to the nodes in the vicinity of a link - that the transmission on
that link consumes. With IRU MIC achieves to control inter-
flow interference.
The following equation is derived after merging two
components of MIC:
∑ ∑+= ii CSCIRU
ETTN
pMIC
)min(*
1
)( (7)
Where N is the number of nodes and min(ETT) is the
minimum ETT in the network which can be based on the
lowest transmission rate of a wireless card.
Yang et al. compared the MIC metric against WCETT and
ETT on the basis of total network throughput, the average end-
to-end delay and maximum channel utilization in both multi
and single channel environments and concluded that MIC has
far better performance than the other metrics[1].
An important point that is not considered in MIC design is
the variability of channel. Many designs take the channel
conditions as static and make their estimations over an average
loss ratio on a link. Channel conditions on wireless links,
however, can be quite instable and can cause packet losses in
bursts. Thus the estimated values for mean loss ratios on a link
will not always be accurate.
h) Frame Transmission Efficiency (FTE)
FTE aims to select paths with reasonable hop count, good
quality and less congestion.
The proposed metric relies on MAC layer retransmissions
caused by congestion or bad quality on a link (i.e. deep
fading). If a RTS or a CTS packet is not acknowledged it
means that there are other nodes contending for the same
channel (traffic contention). If, however, the unacknowledged
packet is a Data frame then it can be deduced that the
retransmission is due to the low quality condition on that
channel.
The calculation of FTE for a link is simple. The researchers,
in order to not to make any modifications on MAC firmware,
used MIB (Management Information Base) variables, such as
ACKFailureCount and RTSFailureCount, respectively for
required number of Data frame retransmissions and RTS
retransmissions.
The number of retransmissions needed to successfully send
its ‘ith’
packet from nodeA to nodeB is defined as
Failure_ab(i):
Failure_ab(i)= ACKFailureCount_ab(i) +
RTSFailureCount_ab(i) (8)
Clearly, Failure_ab(i) represents number of retransmissions of
Data and RTS. Then, the calculation of success rate is
straightforward:
FTE_ab(i)= 1 - Failure_ab(i)/(Failure_ab(i) + 2) (9)
An average of FTEs of a link (A-B) is kept in node A to be
aware of its quality and the congestion level in the vicinity of
this link. This average is estimated over a time period for N
packets sent from node A to node B:
∑=
=
N
i N
iFTEab
FTEab
1
)(
(10)
In addition to FTE, Karbaschi et al.[6] take into
consideration hop count to keep the paths as short as possible,
thus between a source node A and a destination node D:

5. NodeNum
hopCountNodeNum
HopMetric AD
AD
−
= (11)
where ADhopCount is the current minimum number of hops
and NodeNum is the total number of nodes in the system.
Thus the combination of these two metrics becomes:
ADADAD FTEHopMetriccRouteMetri *= (12)
An advantage of this metric is that it piggy backs all the
metric updates on the routing protocols update messages.
Therefore, it does not incur extra traffic overhead on the
network. Interference on the path, however, is not considered
as an evaluation criteria. Another drawback is that this metric
will not be able to react fast to capture the potential changes in
the network topology since it does not take into account the
channel variation or the rapid moves of mobile nodes.
i) Rate, Interference, Packet Success Rate(PSR) metric
Luigi Iannone et al.[5] based their metric design on three
different measurements data rate, interference and packet
success rate (PSR) in an effort to find best paths with large
bandwidth, global network performance, low interference and
reliability.
Their approach is centered on using cross-layer information
obtained from MAC and PHY layers (i.e., SIR) in network
layer, while allowing this layer to manipulate some lower
layer settings(i.e., transmission power, data rate).
Their study refers to Gupta and Kumar’s capacity analysis
for wireless multi-hop networks [27]. According to Gupta and
Kumar the average capacity of such a network is:
nLr
AR
r 2
16
)(
Δ
=
π
λ (14)
where A is the area that a network spans, L is the average
distance between source and destination, R is the maximum
data rate, with transmission range r and total number of nodes,
n in the network. The assumption is that within a distance of
(1+ Δ)r from the transmitting node there should be no other
on going transmissions. The weak interference in this context
is defined as Δ > 0. It is evident that to increase the
throughput the data rate has to be kept as high as possible
while reducing the interference generated by transmission.
Transmission power is the main factor which defines both
interference and data rate. Therefore, the control and
adaptability of transmission power according to changing
conditions (e.g., the location of the next hop) play a very
crucial role in maintaining a high throughput.
Link-quality, however, can not be estimated by using these
metrics, therefore the third metric, PSR, is used on the
network layer along the entire route. This will allow the
network layer to choose an entirely new path in the case of a
serious degradation in channel quality.
The estimation of the interference is difficult. Using a trend
index function, I(.) , which uses local parameters such as
transmission power, P, and the number of nodes, N, reachable
with that level of power, an approximate calculation can be
done. Thus, the smaller the power level or the number of
nodes the smaller the interference produced:
21,PP∀ 21 PP <
I(P1,N) < I(P2,N) (15)
and,
21,NN∀ 21 NN <
I(P,N1) < I(P,N2) (16)
Since we can take the number of nodes reachable as a
function of power level, N(P), the trend function I(.) can be
modelled with a single parameter, the transmission power,
I(P). Then,
P
PP
P
PP
PN
PN
PI
max2
max
max)(
)(
)(
+
= (17)
where Pmax is the max power level and N(Pmax) is the
maximum number of nodes reachable with this power level.
Then the interference on a path can be written as:
∑∈∀
=
Pathji
jiji PIPathI
),(
,, )()( (18)
In addition to interference metric, the PSR (Packet Success
Rate) is estimated as follows:
∏∈∀
−=
Pathji
jiPERPathPSR
),(
)),(1()( (19)
where PER(i,j) is packet error rate on a link between nodes i
and j.
As in various studies done, the proposed metric is combined
into a form to find the cost for the best paths, C(path):
)(
)().(
)(
pathRate
pathPSRpathceInterferen
pathC = (20)
The authors, however, assert that using the metrics in this
way may not be correct since combining them in such a
compact equation will not always lead to accurate results in
path estimation. Therefore, they propose to use these metrics
separately on the network layer and splitting the routing
protocol tasks into two, such as Power optimization and Route
Discovery. According to this mechanism, after the nodes
discover their neighbours, they apply the most suitable
transmission power, for each node, offering the optimum
trade-off between PSR and Interference.
As their work does not include simulations or results we can
not comment on their estimation techniques and indicate if
their metrics have drawbacks or advantages. The idea of

6. including interference, success rate and data rate, on the other
hand, is a relevant and indispensable approach on designing
path selection metrics.
j) Radio-Aware Path Selection Metric (Proposed in WMNs
Draft)
The recently released WMNs draft proposes a radio-aware
path selection metric as the default path selection metric [14].
The proposal, however, does not imply any obligation on
potential implementations to use the default metric.
Accordingly, any implementation may use other metrics
besides the default metric.
In this scheme, routing tables are populated by using link
state information estimated by each node in the network. To
achieve this, MPs calculate the pairwise link costs over a path.
The paths are selected on air time cost basis. Air time cost
function is an approximate estimation of channel resources
consumed by transmitting a packet over a particular link.
pt
pcaa
er
B
OOc t
−⎥
⎦
⎤
⎢
⎣
⎡
++=
1
1
(21)
caO , the channel access time, pO , the protocol overhead, and
t
B , test frame size, are constant and their values are indicated
in Table 1. The input parameters r and pte are the bit rate in
Mbit/s and the frame error rate for a test frame of size
t
B
respectively. The bit rate selection of r is a conditional local
decision defined by the implementation, where as the pte is the
frame corruption probability with a given rate r and frame size
t
B .
TABLE 1
Paramet
er
Value
(802.11a)
Value
(802.11b)
Description
Oca 75µs 335µs Channel access
overhead
Op 110µs 364µs Protocol overhead
Bt 8224 8224 Number of bits in
test frame
Figure 2 depicts a small-size network with air time costs
indicated on the links.
48Mb/s, 10%
PER
54Mb/s, 8%
PER
12Mb/s,
10% PER
54Mb/s, 2%
PER
54Mb/s, 2%
PER
48Mb/s, 10%
PER
Figure 2. Example Unicast Cost Function based on Airtime Link Metrics
The proposed metric on the draft [14] takes bandwidth and
loss rations into account. It fails, however, to address the
interference issue and how it can be handled, as well as, the
potential rapid changes that may occur on channels. Besides,
the details about incorporating mutli-channel/multi-radio
aspects into the proposed metric are not given, therefore we
can not comment if this metric will conform with WMN
requirements.
k) Metric of Modified ETX (mETX) and Effective Number of
Transmissions (ENT)
Koksal et al. [4] base their work on ETX metric. They assert
that ETX functions work well when the wireless channels are
relatively static and does not take into consideration that these
channels can be highly variable in short-term. For example,
these channels may have low loss ratios with high variability
which, eventually, will cause metrics that account for mean
loss ratios to pick less desirable paths.
The proposed metric has two facets. The first part of the
proposed metric is called mETX, a modified version of ETX
which takes into account the short-term variations on the
channel state. The second part, ENT (effective number of
transmissions), in addition, tries to find paths with the highest
potential of inducing high network throughput. Furthermore, it
attempts to meet requirements of higher layer protocols (i.e.
TCP) by keeping the end-to-end loss rate as low as possible,
so that the end-to-end retransmissions do not occur.
Minimizing the number of transmission is a good way of
maximizing the overall network throughput as ETX metric
tries to achieve. The authors, however, assert that ETX, by not
taking the channel variability into consideration, may lead to
inaccurate results since it estimates the channel only by its
average behaviour and define an ETX as a geometric random
variable which implies that all the packet losses are
independent from each other. In many studies however, as the
authors indicate in [4], it is proved that the packet losses occur
in bursts rather than individual basis. The incurred loss
probability, in addition, is not constant.
In order to overcome above problem Koksal et al. model a
time varying binary symmetric channel where a bit transmitted
at time t is misdetected by the receiver with probability tBP ,
.

7. They assume a stationary process, { 1,, ≥tP tB
}, which is
independent from the channel input. tBP ,
represents a sample
outcome of a random process with each sample, tBp ,
, falling
between 0 and 1.
The absence of a link layer ACK means that the receiver
has found a bit error on the received packet and dropped it.
The sender, in return, sends the same packet until it is
successfully delivered. If, however, these errors repeat, M
times (M retransmissions by the sender) then the error
becomes visible to the higher layer protocols (i.e. TCP) and
the packet may be resent end-to-end.
In order to estimate the probability where all bits on a
packet delivered error-free, the proposed model introduces a
discrete stationary process { 1,, ≥kP kc } which is defined as:
∏
−+
=
−=
1
,, )1(
St
tt
tBkc
k
k
PP (21)
where S is the packet size and tk is the starting time for the
transmission of the kth packet. Thus, kcP,
represents the
conditional probability that bits tk,….,tk+S – 1 were
transmitted without any error. Therefore the unconditional
probability that the corresponding packet has no errors is
E[ kcP ,
].
In order to evaluate the expected number of transmissions
(ETX) in case where there maybe possible dependence on bit
errors, the authors introduce the instantaneous number of
transmissions, kcP ,/1 . Then using Eq(21),
)exp(
1 1
,
,
∑
−+
=
=
Stk
tkt
tB
kcP
η (22)
where tBtB P ,, ≈η for reasonably small values of tBP , . Letting
∑∑
−+
=
=
1
,
Stk
tkt
tBk η and after some probabilistic manipulation(see
[4]), the modified ETX, mETX, is defined as:
)
2
1
exp( 2
∑∑ += σµmETX (23)
where ∑
µ and ∑
2
σ represents the average and the variability
of the error probabilities, respectively. The first term is
sufficient to estimate the long term average level channel bit
error probability and is similar to ETX. The second term, on
the other hand, helps estimate the short term channel error
probability variations on the link.
The ENT, unlike mETX, aims to optimize the aggregate
throughput by bounding the packet loss rate visible to higher
layer protocols. For this end, links selected should not be
subject to high loss ratios, since a high loss ratio causes the
link layer retransmissions, after a certain number of times,
cease (in a good link layer protocol) and make the loss visible
to the higher layer protocol. Accordingly, ENT estimates the
probability that number of link layer retransmissions are under
a certain threshold, M:
)/1( , MPPP kcloss >= (24)
If an application, say TCP, requires that on a given link lossP
should stay under a given loss probability constraint,δ , then
the link should satisfy (see [4] for more informative derivation
of the equation),
Mlog2 2
≤+ ∑∑
δσµ (25)
This time, the first term on the left hand side represents the
impact of the slowly varying and the static state of the channel
whereas the second one reflects the rapid channel variations
(at the packet time scale). The equations simply implies that
for packet losses to remain invisible to the higher layers, the
sum of two entities, which can be thought as the logarithm of
the sum of effective number of transmissions (i.e. logENT),
must stay below the threshold, Mlog .
The estimations of these two metrics are done in a similar
way to the ETX except that the data is collected over bit level
rather than the packet level. Each node broadcasts a probe
packet every 10 seconds to calculate a loss rate sample which
in turn passed to an exponentially weighted moving average
filter. The average and the variability of error probabilities are
estimated by considering the locations of erred bits in each
probe packet.
Both mETX and ENT achieve to include time varying
characteristics of the channel which can be translated into
network and application layer quality constraints. Both
metrics, however, inherit the same weaknesses that ETT has
since they are built over this metric. Thus, interference issue
as well as underestimation of data and overestimation of ACK
loss ratios seem not to be addressed. The latter is due to link
estimations which are done in a similar way as in ETX (i.e.
single probe packet size of 134bytes). Besides, since authors
designed their metrics for WMNs, it would have been more
insightful if the multi channel/multi radio nature of have been
addressed.
B. Power saving and Energy Efficiency-based Metrics
Unlike the link reliability and network performance-based
metrics so far discussed, power saving and energy efficiency
based metrics are designed mainly for maximizing the lifetime
of nodes and overall network by using energy conserving
techniques.
The lifetime of a node in a network becomes a vital point
when the network nodes are mobile. In a mobile wireless
network, nodes have limited power supply defined by their
battery capacity. Connectivity problems and network
partitioning may easily occur when some of the network nodes
are discharged of their battery power. It is expected that
battery technology is unlikely to advance as rapidly as
computing and communication technologies [19], [13], thus
protocol design oriented towards power saving and energy
consumption is vital in the context of mobile wireless
networks.
Power-aware routing protocols could be broadly classified
into two categories; namely activity based and connectivity
based protocols [13].Activity based protocols address the issue

8. of power consumption as it relates to network activity i.e. the
actual transmission of data between nodes in the network.
These protocols make routing decisions based on power
consumption which results in the actual transmission of data.
Typical path selection criteria under activity based protocols
are subject to conditions such as minimal per packet energy
consumption and maximal overall network lifetime. On the
other hand, connectivity based protocols focus on maintaining
effective network connectivity while attempting to reduce the
power consumption. The reduction in power consumption is
basically achieved by transmission power adjustments
(control) in order to save energy or turning off some idle
nodes (sleep mode) while maintaining the effective network
connectivity[13].
In wireless mesh networks, however, most of the
estimations are built on the fact that the nodes are mostly static
Mesh Points (MPs). Therefore, during the process of
designing a metric for WMNs, energy efficiency seems to
have a little importance, at first sight. Nonetheless, since we
are to deal with mobile MPs in a WMN, it might still be an
interesting approach to incorporate energy-based metrics with
a focus on node activity in the process of metric design for this
kind of networks.
a) MPR: Minimum Power Routing
Minimum power routing [20], was one of the initial
approaches of dynamic power aware routing schemes
proposed, based on the physical and link layer statistics. The
aim was to route a packet along a path with minimum total
power consumption and for each node to transmit with just
enough power to ensure reliable communication. The proposal
addresses the reliability aspects such that a high packet
success rate is to be achieved by maintaining an acceptable
signal-to-noise ratio (SNR) at the receiver. The transmission
power from node i to j,
ijTP , is determined by,
η
ε
−
=
ijij
T
rS
Pij
, (26)
where ε is the desired bit-energy-to-noise-density ratio at node
j, Sij is the dynamic link scale factor reflecting the current
channel characteristics and interference on link ij, rij is the
distance between i and j, and η is the path loss exponent. The
cost function assigned to every link reflecting the transmitter
power required to reliably communicate on that link is given
by,
⎪⎩
⎪
⎨
⎧
=
≤++
∞
,)1()........1(
............
maxPPifP
otherwise
ij
ijTijT
C
κκ
(27)
where κ is the dampening constant which provides extra
margin for the transmission power limited by Pmax. It is a
design parameter that must be selected (See [20] for complete
derivation).
Subbarao
claims
that
this
initial
approach
shows
promise
as
a
power
conscious
routing
scheme
which
adapts
to
the
changing
conditions
and
interference
environment
of
a
node.
b )PARO: Power-Aware Routing Optimization
PARO [21], reduces the transmission power by maximizing
the number of intermediate redirector nodes between the
source and the destination (see Figure 3).
Figure 3. Energy saving by intermediate forwarding
The work was based on basic link assumptions that nodes are
having radios capable of dynamically adjusting the
transmission power (e.g. commercial radios that support IEEE
802.11 and Bluetooth with power control capability) on per
packet basis and the nodes in the network are capable of
overhearing any transmissions by other nodes as long as
received SNR is above a certain minimum value.
A node keeps its transmitter “on” to transmit a data packet to
another node for L/C seconds, where L is the size of the
transmitted frame in bits and C is the raw speed of the wireless
channel in bits/second. Similarly the receiver node keeps its
transmitter “on” to acknowledge a successful data
transmission for a combined period of l/C seconds where l is
the size of the acknowledgement frame.
The aggregate transmission power to forward one packet
along an alternative route k, Pk is defined by,
ClTLTP iiii
N
i
k
k
/)( ,11,
0
++
=
+= ∑ , (28)
where Tij is the minimum transmission power at node i such
that the receiver node j along the route k is still able to receive
the packet correctly, while Nk is the number of times the data
packet is forwarded along the route k. In addition to the
transmission of the data packets with minimal power Pk,
PARO utilises a portion of its transmission power for route
discovery process. If the corresponding transmission power
consumed by the routing protocol to discover the route is Rk,
the cost function for transmitting Q packets between a given
source –destination pair along the best route k is defined by,
ClTLTQRC iiii
N
i
kk
k
/)( ,11,
0
++
=
++= ∑ (29)
PARO accommodates both static and mobile environments
[21].Authors claim that in the case of static networks, once a
route has been found there is no need for route maintenance
unless some nodes are turned off. Moreover, under heavy
traffic conditions (e.g. large Q) cost of data transmission
outweighs the cost of finding the best power efficient route
(Rk).In the case of mobile environments, however, there is a
need for route maintenance.
a
b
c

9. Although these schemes ([20], [21], [28]), attempt to reduce
the transmission energy consumption, they do not reflect on
the lifetime of each node. As argued by [13] such active
power-aware routing protocols may tend to overuse subset of
nodes, given the goal of minimizing the energy consumption.
In order to consume node energy in a more balanced
manner, the node residual energy based schemes have been
proposed.
c) MBCR: Minimum Battery Cost Routing
The battery cost function defined as,
t
i
t
ii
c
cf
1
)( = (30)
Where
t
ic is the remaining battery capacity of node i at time t
and the battery cost for route j with Dj number of nodes is,
∑
−
=
=
1
0
)(
jD
i
t
iij cfR (31)
The route that has the minimal battery cost (maximum
battery capacity) is chosen as the best route, [22] [23]. Singh et
al. claims that the battery characteristics could be directly
incorporated into the routing protocol in such a way that the
node costs are updated constantly and when a packet is
transmitted over one hop, the current node cost is added to the
total cost of the packet.
d) MMBCR: Min-Max Battery Cost Routing
MMBCR is based on MBCR and attempts to mitigate the
usage low-energy nodes in path selection process. It was noted
by Toh, Kim et al that when the path cost is calculated as
described above, it may lead to situations where nodes with
very little remaining battery capacity can still be selected if the
rest of the nodes along the route have large residual capacity.
MMBCR is proposed to address this problem where the
battery cost of the route j is defined as,
)(max
_
t
ii
jroutei
j cfR
∈
= (32)
where )( t
ii cf is the inverse residual battery capacity(as in
MBCR).The desired route ro is chosen such that,
j
rjroute
o RrR
∗∈
=
_
min)( (33)
where ∗
r is the set of all possible routes from the source to
destination nodes in discussion.
Figure 4. MMBCR path selection
As illustrated in Figure.3 the desired route, R2 between node
S and node D is preferred based on min-max metric described
above. It could be noted that even though the route, R1 has a
higher path cost (of 10) according to MBCR, it contains the
node with the minimal battery cost(1) which makes it
disqualified under MMBCR scheme.
d)
CMMBCR:
Conditional
Min-­‐Max
Battery
Cost
Routing
MMBCR
mechanism
does
not
guarantee
the
minimal
per
packet
total
transmission
power
consumption
over
a
chosen
path.
A
hybrid
approach
(CMMBCR)
was
proposed
in
order
to
meet
both
total
transmission
power
consumption
and
battery capacity goals.
A threshold, γ is defined to describe the
sufficient battery capacity of all the nodes in candidate routes.
A route with minimum total transmission power (MTPR), [28]
is chosen among these candidate routes [24], [23].(As the
name implies MTPR simply selects the minimum total energy
path between a source destination pair).
If the battery capacity of route j is,
t
i
jroutei
c
j cR
_
min
∈
= (34)
and if there exists a set(A) of all routes between any two nodes
satisfying, γ≥c
jR amongst all possible routes(Q) between
the same two nodes; then the minimum total transmission
power routing scheme[ applies. Otherwise, a route with the
maximum battery capacity is chosen.
}{ }QjRR c
j
c
j ∈= max (35)
The
main
drawback
of
the
scheme
is
that
there
is
no
known
method
to
efficiently
determine
γ. Also this requires
either a centralized server to keep track of energy status of all
the nodes or each node must update one another about the
remaining power status of each of them.
Drain
Rate
Mechanism
Kim et al. noted that metrics related to node residual energy
or remaining power mechanisms alone can not be used to
establish best routes. For example, if a node accepts all route
requests merely because it has enough residual battery
capacity, the battery of that node will drain off quickly as a
result of the high traffic load injected through it). Hence, the
battery drain rate (energy dissipation rate) is also taken into
account in the definition of cost function.
Each node monitors its energy consumption caused by
transmission, reception and overhearing activities and
computes the energy drain rate (Actual DRi of node ni is
calculated using EWMA).The corresponding cost function is
defined as,
S D2
3
2
R2=3
2
R1=7
1 7

10. i
i
i
DR
RBP
C = (36)
Where iRBP is the residual battery power of node ni.
The maximum lifetime of a given path corresponds to,
i
rn
p CL
pi∈∀
= min (37)
The minimum drain rate scheme (MDR) will select the
route with the highest lifetime.
A scheme similar to that of CMMBCR was proposed to
take the minimum total transmission power into account,
where nodes with a life time higher than a given threshold,
i.e., δ≥
i
i
DR
RBP
form all possible paths. The advantage in this
scheme is that δ can be chosen as an absolute time value to
represent how a node can sustain its current traffic condition
(unlike the ambiguity in deciding on γ under CMMBCR
method).
The implementation of the proposed metric was based on
technology described by Smart Battery System
Implementation Forum [25].
Furthermore, authors note that not all the RBP is available
for the wireless interface and it is important to consider the
realistic portion of RBP used by the wireless interface (18-
20% as suggested by [26], [23]).
III. ROUTING IN WMNS
Routing protocols for wireless networks have long been
an active research area. The emerging of mobile ad-hoc
networks triggered the devising of routing protocols for highly
dynamic wireless network topologies. So far, various types of
routing protocols have been created; among them most
popular are AODV, DSR, OLSR [8], DSDV, and LQSR [18].
Depending on the time the routes are calculated routing
protocols are dived into two classes: reactive and proactive
routing. In reactive protocols, paths are discovered when a
source node needs to send a packet to a destination node. In
order to keep the network connectivity tight against the high
potential of link breakages in mobile wireless networks,
flooding method is used. Proactive routing protocols, on the
other hand, calculate all the routes before any data exchange
takes place. Nodes keep routing tables updated with each
change in the network topology by propagating update
messages throughout the network. Proactive routing can be
subdivided in to two classes of routing scheme: source routing
and hop-by-hop routing. In source routing, forwarding of a
packet is done by just checking the header of a packet. The
exact route that a packet is supposed to traverse is embedded
in the header of that packet. In hop-by-hop routing, forwarding
is achieved according to the local information that is present in
the forwarding node’s routing table. Each node keeps the next
hop information in the table for every destination in the
network. However, the existing routing protocols that treat all
the network nodes in the same way may not be efficient
enough for WMN s because mesh routers in the WMN
backbone and mesh clients have significant differences with
respect to power and mobility constraints[3].
Apparently, nodes in WMNs have less “mobility” and
therefore have less energy dependency than ad-hoc networks.
This first superficial analysis of WMNs may give inclination
to prefer a proactive routing scheme over a reactive one.
However, as it was stated earlier WMNs do not have an
entirely static or a mobile characteristic. Besides proactive
protocols compared to reactive ones inject high overhead on
the links. The scalability is another problem with them, though
the optimized link state protocol, OLSR, have mechanisms to
overcome both of these drawbacks and is appropriate to be
used in WMNs. In the proposed WMNs draft, AODV is
defined as the default routing protocol to be used in Hybrid
Wireless Mesh Protocol (HWMP) [14] whereas OLSR is
proposed as an optional routing protocol to be employed in
Radio Aware OLSR Path Selection Protocol.
As it was previously discussed in the second section, there
are various requirements for a routing protocol to take into
account. One of them is being careful about selecting a
specific route which may cause unwanted consequences on the
overall throughput of the network. For example both sending
traffic over selected paths and gathering information during
the selection phase of those paths consumes channel resources.
In addition to these, the interference created by the transfer of
probe and data packets shrinks down the available bandwidth.
Thus, reducing the number of messages exchanged during
route discovery or maintenance is an important requirement
for a routing protocol to be employed in WMNs. Furthermore,
when multi-radio or multi-channel wireless mesh nodes are
considered, the routing protocol should be capable of selecting
the most appropriate channel or radio on the desired path and
obviously it becomes a cross-layer design as change of a
routing path involves the channel or radio switching [3].There
may be other requirements imposed by application layer to be
met, such as quality of service, security, interoperability,
power consumption etc… Thus, having application layer
requirements in addition to lower layer requirements obliges
researchers to be more cautious while designing routing
metrics and protocols for WMNs.
IV. DISCUSSION
The metrics that are studied throughout this report and the
many others in the literature are mostly based on network
performance. The energy-based metrics or routing, on the
other hand, is mostly concerned about life time of mobile
nodes in a network. Since we are mainly concerned about
WMNs which are mostly formed by static nodes, we chose to
put less emphasis on energy conservation in this survey.
However, some power-aware schemes that address problems
such as interference and varying channel conditions may be
amalgamated with network performance based metrics in
focus.
A crucial point related to this survey study was to put more
weight on using cross layer information in identifying
optimum routing paths. In order to have improved
performance, routing protocols need to exchange information
with lower layers. Therefore the report stresses more on the
routing mechanisms that are using multiple performance
criterion captured in lower layers and incorporated in the
routing layer.

11. The central point of attention in performance-based metrics
that are studied in the report are mainly link loss rates,
consumption of channel resources, intra and inter-interference,
delay and therefore the load on a link. Among them ones that
are based on link loss ratios combined with bandwidth
consideration on a particular link were found most successful.
The pioneer of this type of metrics was ETX which evolved to
be ETT with the bandwidth aspect incorporated in the metric
calculation. Followers of these metrics based their metrics
design mostly on ETX and combined it with interference
information in order to pick channels that are less likely to be
interfered by self-interference and inter-flow interference.
Some researchers [5], on the other hand, reported that it is not
always practical or feasible to combine a set of metrics into
one compact metric because those metrics may not be
compatible with each other or have downward effects on the
routing protocol. Such situations require that the metrics must
be used separately in order to not to cause incoherency among
the metrics and in the calculation of the routes in the network
layer.
Among all the metric design approaches we have studied in
this report load balancing (i.e. multipath routing, congestion
aware routing) alongside with lower layer parameters have
never been used, neither energy-conservation based metrics
are attempted to be combined with any other performance
metrics. Moreover, since we are especially concerned with
WMNs which is composed of mesh points with multi
radio/multi channels, we believe that there should be more
effort on research should be given on taking these aspects into
account. So far, metrics other than WCETT and MIC (based
on WCETT) seem not to be concerned with multi radio and
multi channel technology.
Other than these we believe that in WMNs for a metric to
find the optimum paths one should seriously address the
interference issue by employing alternative approaches
besides simply estimating interference on the links. For
example, in order to help routing metrics to function better
with the routing protocols and therefore increase network
performance, radio power control, as well as directional
antennas may be employed on the nodes. Multi-channel usage
and good channel assignment should be also considered
profoundly.
Our future work will be based exploring most suitable
performance metrics for WMNs along side with energy-
based/power-aware ones. We want to analyse the combined
performance of these two classes of metrics. As a further study
we want to focus more on design of metrics with a focus on
interference used in directional antenna environment.
V. CONCLUSION
In this report, we have presented a survey on a collection of
routing metrics. We studied the requirements for the design of
a “good” performance metric that is highly likely to select the
optimum paths between a source and a destination node. We
pointed out the drawbacks and strong points of these metrics
and compared these points with each other. Furthermore, we
have made a summary of selected power-aware and energy-
conservation based metrics, and indicated their pros and cons.
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