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SOURCE:
Telenor Research & Innovation,
1331 Fornebu,
Norway
Analysis and Measurements of the Throughput in IEEE 802.11 Mesh
Networks
Vegard Hassel
Telenor R&I
B7d
1331 Fornebu
NORWAY
Phone: + 47-97159122
Fax:
+ 47-91509001
Email: vegard.hassel@telenor.com
Analysis and Measurements of the Throughput
in IEEE 802.11 Mesh Networks
V. Hassel, T. O. Breivik, P. E. Engelstad, and L. Henden
Telenor Research & Innovation, 1331 Fornebu, Norway
Abstract – It is well-known that the throughput of wireless
mesh networks without frequency re-use decreases as O(1/N),
where N is the number of nodes in the network. In this paper
we build on this result and obtain expressions for calculating
the throughput in IEEE 802.11-based mesh networks without
interference. Both expressions for single-frequency and multifrequency mesh networks are obtained. We compare the
analytical results with measurements of the UDP throughput in
a real IEEE 802.11 mesh network, and show that our analytical
expressions can closely approximate the throughput in real
mesh networks.
I.
INTRODUCTION
Several major cities have deployed IEEE 802.11-based
wireless mesh networks (WMNs) during the last couple of
years. In such networks packets are forwarded wirelessly
between neighboring access points so that only a percentage
of the access points in a network need to have wired
backhaul. Although the deployment costs of such networks
will be lower compared to networks with wired backhaul to
all access points, the throughput will be lower since a share
of the capacity is used to forward packets. Wi-Fi mesh is
currently being standardized as the IEEE 802.11s standard,
thus, the Wi-Fi mesh equipment currently on the market is
proprietary. In this standard, clients or users are referred to as
stations (STA) and access points or nodes that have the
ability to both serve STAs and forward packets to
neighboring access points are referred to as Mesh Access
Points (MAPs). In this paper we will use this notation.
Several papers have analyzed the capacity of ad hoc and
mesh networks. Ad hoc networks are wireless networks
where nodes are communicating with each other via other
nodes in the network, and Gupta and Kumar have obtained
some general results for how the capacity between an
arbitrary pair of stationary nodes in ad hoc networks with
frequency re-use scales with the number of nodes in the
network [1]. They have shown that if the nodes are optimally
placed in a disk of unit area, the traffic patterns are optimally
assigned and each transmission’s range is optimally chosen
the throughput obtainable by each node scales as Θ W N ,
where W is the throughput that can be obtained by each node
on a common wireless channel and N is the number of nodes.
The results of Gupta and Kumar have been generalized to
nodes with multiple radios in [2].
WMN can be seen as a type of ad hoc network. However,
there are two main differences between ad hoc networks and
WMNs. In an ad hoc network, the nodes can be mobile while
the MAPs in a WMN are fixed. In addition, the
communication within an ad hoc network is often assumed to
be kept within the network while a WMN is often used to
(
)
provide access to external networks, e.g. the Internet. In a
WMN, at least one MAP, a so-called gateway or Mesh portal
Point (MPP), is connected to the external network.
Most of the research related to WMNs has been on
different routing and scheduling algorithms. Only a few
papers have obtained expressions for the throughput of
WMNs [3-4]. In [3] the authors have proved that the
throughput of WMNs decreases as O(1/N) in networks
without frequency re-usage, where N is the number of MAPs
in the network. This result does not take into account that the
throughput between the MAPs is often different from the
throughput between a MAP and a STA. In addition, the
derivation in [3] does not take into account that the
throughput of the wireless links between different MAPs can
be different. Consequently, we provide an extension of the
results in [3] in order to obtain more realistic throughput
estimates for real WMNs. We show that our analytical
expressions closely estimate the WMN throughput in
environments with limited interference.
In Section II we outline the system model. In Sections III
to V we provide derivations of different analytical
expressions, while in Section VI we compare plots from the
analytical expressions with measurements performed in a
real-life mesh network. Conclusions and future work are
handled in Sections VII and VIII.
II.
SYSTEM MODEL
We assume that we have a WMN with N MAPs
communicating based on the IEEE 802.11 standard. The
placement of the MAPs in a WMN is fixed and for short
periods of time it can therefore be assumed that the traffic
between the MAPs is routed in static routes. The WMN can
therefore be seen as a small autonomous network
constituting one gateway and all the MAPs sending traffic to
and from this gateway.
The bitrate between the MAPs is assumed to be equal to
Rn for all links and the bitrate between a MAP and its
associated STA is equal to Rc in all cases. For our analytical
framework we assume that no intra- or inter-network
interference influence the network. This means that we have
assumed that there will be no loss from collisions in the
CSMA/CA MAC protocol in the IEEE 802.11 standard.
We also assume that the WMN has a fairness mechanism
for allocating throughput to the STAs. The total available
transmission time is therefore divided between the time used
to forward packets between MAPs and the time used to serve
STAs in such a way that all the STAs receive the same
throughput. Such fairness mechanisms are common in WMN
equipment based on the IEEE 802.11 standard.
III.
DERIVATIONS OF ANALYTICAL EXPRESSIONS FOR
SYMMETRICAL, SINGLE-FREQUENCY WMNS
In this section we derive expressions for WMNs where the
available bitrates between the MAPs are identical and equal
to Rn and the bitrates between the MAPs and the STAs are
identical and equal to Rc. We denote this kind of networks
symmetrical WMNs. Fig. 1 shows a symmetrical WMN with
a chain topology. The WMNs investigated in this section are
single-frequency which means that the same channel, or
frequency, is used for all links between the MAPs and for the
links between the MAPs and the STAs.
B. A Chain of N MAPs with one STA each
Figure 3. Symmetrical mesh network with N MAPs in a chain topology. One
STA is communicating with each MAP.
Fig. 3 shows a chain of N MAPs with a gateway in one
end and a STA connected to each of the MAPs. For this
topology we can state the following equations for a fully
loaded network with no frequency re-use:
Rc ⋅ t c = R n ⋅ t n
Figure 1. Symmetrical mesh network where the bitrates between the MAPs
are identical and equal to Rn and the bitrates between the MAPs and the
STAs are identical and equal to Rc.
N −1
Nt c + t n ∑ i = Nt c +
i =1
( N − 1) N
tn = 1.
2
(4)
(5)
The reasoning behind Eq. (5) is that tn seconds is used for
forwarding traffic to each of the STAs further out in the
chain. Consequently, the gateway MAP will have to forward
traffic intended for N-1 STAs. If Rc and Rn are assumed to be
known, the maximum throughput offered to each of the
STAs can be expressed as:
A. One STA at the end of a Chain of N MAPs
Figure 2. Symmetrical mesh network with N MAPs in a chain topology. The
gateway is placed in one end of the chain and a STA in the other end of the
chain.
TPmax = Rc ⋅ t c =
Rc
.
( N − 1) N Rc
N+
2
Rn
(6)
C. General Mesh Topology
Fig. 2 shows a chain of N MAPs with a gateway in one
end of the chain and a STA connected to the MAP in the
other end. For this topology we can state the following
equations for a fully loaded network with no frequency reuse:
Rc ⋅ t c = R n ⋅ t n
(1)
t c + ( N − 1)t n = 1 ,
(2)
where tc is the time used to transmit data between the MAP
and its associated STA and tn is the time used to transmit
data from one MAP to the neighboring MAP. For these
equations it is supposed that all the MAPs interfere with each
other and none of the MAPs can transmit simultaneously.
This not an entirely correct assumption since channels can be
reused at certain intervals. If Rc and Rn are regarded as
known, the maximum throughput offered to the STA can be
expressed as:
.
(3)
Rc
TPmax = Rc ⋅ t c =
Rc
1 + ( N − 1)
Rn
For Rc=Rn=R, this expression reduces to the well-known
expression TPmax=R/N, which was first derived in [5].
Figure 4. Symmetrical mesh network with a general topology.
Fig. 4 shows a general mesh topology based around one
gateway. For this topology we can state the following
equations for a fully loaded network with no frequency reuse:
Rc ⋅ t c = R n ⋅ t n
(7)
tc + 3(tc + tn ) + 6(tc + 2t n ) = 1
(8)
.
Rc
TPmax = Rc ⋅ tc =
10 + 15
(9)
Rc
Rn
These equations show that it is possible to approximate the
maximum rate in any fully loaded WMN with no frequency
reuse. Since most WMNs are deployed with few hops from a
MAP to the nearest gateway, the analytical framework above
can be used to approximate the real throughput in most
WMNs. In the next section we will explain how our
analytical framework can be modified to take frequency reuse into account.
D. Taking Frequency Re-Use into Account
Our measurements show that intra-network interference in
an IEEE 802.11-based mesh networks will be limited after
four hops. This means that for the WMN in Fig. 1, MAP
number 1 can transmit simultaneously as MAP number 5 and
MAP number 2 can transmit simultaneously as MAP number
6. For this case it can be shown that it is indifferent if this
time is used to serve clients or if the time is used to serve the
next MAP. If we assume that Rc>Rn for the network in Fig. 1,
we will have tc<tn, and we obtain the following equations:
3
4tc + tn ∑ i + tn ∑ i = 1
i =1
TPmax = Rc ⋅ t c =
(11)
i =1
.
Rc
4+9
(12)
Rc
Rn
We can now use the same reasoning as outlined in the
previous sections to calculate the throughput of any WMN
topology. As a rule of thumb the number of hops from the
gateway should not exceed three in a single-frequency mesh
network. The number of MAPs per gateway is therefore
limited and it is relatively simple to calculate the throughput
for the MAP cluster belonging to one gateway. When
planning single-frequency mesh networks it is often useful to
use different frequencies for different clusters. The
interference between neighboring clusters is therefore limited
and consequently our expressions will give good estimates
for the throughput also for larger WMNs.
IV.
Rn1 ⋅ t n1 = Rn 2 ⋅ t n 2 = Rn 3 ⋅ t n 3 = Rc1 ⋅ t c1 =
Rc 2 ⋅ t c 2 = Rc 3 ⋅ t c 3 = Rc 4 ⋅ t c 4 = B
DERIVATIONS OF ANALYTICAL EXPRESSIONS FOR
ASYMMETRICAL, SINGLE-FREQUENCY WMNS
(13)
4
3 ⋅ t n1 + 2 ⋅ t n 2 + t n 3 + ∑ t ci = 1 ,
(14)
i =1
where tni is the time used to transmit data to one STA on the
link with bitrate Rni, tci is the time used to transmit data to
one STA on the link with bitrate Rci, and B is the number of
bits that are transmitted on the different links to each of the
STAs. Assuming that the rates of each of the links are known,
combining Eqs. (13) and (14) gives:
B=
(10)
Rc ⋅ t c = R n ⋅ t n
2
In many WMNs, the bitrate between two MAPs and
between a MAP and a STA are unequal. We refer to such
networks as asymmetrical WMNs. When the network above
is fully loaded, we can state the following two equations for
the asymmetrical WMN shown in Fig. 5:
1
.
4
3
2
1
1
+
+
+∑
Rn1 Rn 2 Rn1 i=1 Rci
(15)
From Eqs. (13) and (15) it is now simple to find the values of
tci and tni for different values of i. Designing algorithms that
allocates these values of tni and tni for a WMN will give the
maximum throughput for the WMN, when the throughput
offered by each of the MAPs is equal. Similar equations can
be stated for any WMN topology. For WMNs with frequency
re-use, the principles from Section III.D can be used.
However, this will be a more challenging exercise for
asymmetrical bitrate WMNs since the transmission times on
the different links will vary from link to link.
V.
DERIVATIONS OF ANALYTICAL EXPRESSIONS FOR
MULTI-FREQUENCY WMNS
A. Dual-Frequency WMNs
Dual-frequency WMNs use one frequency or channel for
the links between the MAPs and one frequency for serving
the STAs. Typically, a dual-frequency mesh uses the IEEE
802.11a standard in the inter node connection and the IEEE
802.11b/g standard to serve the clients. For such networks,
two radio interfaces are implemented per node and the internode connection can forward packets at the same time as the
clients are served. The maximum throughput in the network
is limited by:
TPmax= min(TPc,TPn),
(16)
where TPc is the average throughput offered to the STAs and
TPn is the average throughput in an inter MAP connection.
E.g., if the general mesh in Fig. 4 is based on dual-frequency
technology the throughput will be given as:
Figure 5. Asymmetrical mesh network where the bitrates between the MAPs
are unequal and the bitrates between the MAPs and the STAs are unequal.
R R 
TPmax = min  c , n  .
 10 15 
(17)
B. Triple-Frequency WMNs
In triple-frequency WMNs, the MAPs typically use one
frequency for serving the STAs, one frequency for sending
data to other MAPs (egress traffic) and one frequency for
receiving data from other MAPs (ingress traffic). For such
networks the maximum throughput in the network can also
be expressed by using Eq. (16), however, the value of TPn
will typically be higher compared to dual-frequency mesh
networks.
VI.
each of the STAs. Fig. 6 shows the received UDP throughput
as a function of the UDP traffic sent from the gateway, when
traffic was sent to one STA at a time in an area with limited
interference. The highest error-free throughput is found at
the point where the graphs are starting to curve.
RESULTS FROM UDP THROUGHPUT MEASUREMENTS
IN AN IEEE 802.11-BASED WMN
This section will describe results that have been obtained
through measurements with Tropos MetroMesh 5210 MAPs.
These MAPs are single-frequency MAPs based on the IEEE
802.11b and IEEE 802.11g standards. Since the IEEE
802.11s standard is not yet finalized, the MAPs used in our
measurements are based on some proprietary protocols for
the transmission and routing between the MAPs. To limit the
influence from proprietary protocols, the measurements were
performed for a chain of MAPs, where each MAP could only
send traffic to their neighboring MAPs. This was ensured by
having line-of-sight between neighboring MAPs and non
line-of-sight between MAPs that were not neighbors in the
chain and adjusting the placement of the MAPs. In addition,
the STAs were placed at the same location as the
corresponding MAPs so that the channel quality between a
MAP and a STA was relatively stable.
A. Measurements in a Network Based on IEEE 802.11b
The first set of measurements was performed for a chain of
six MAPs where the bitrate at the PHY layer between two
MAPs were fixed to 11 Mbit/s. One STA was placed less
than a meter from each of the MAPs. The STAs
communicated via IEEE 802.11b PCMCIA cards and
because of the proximity between STA and MAP, it was
probable to assume that the PHY bitrate between the STA
and their corresponding MAPs was 11 Mbits/s.
In the analytical expressions presented above, it is
assumed that the values of Rc and Rn are known. Since we
wanted to measure throughputs on the UDP layer the values
of Rc and Rn would represent bitrates on the UDP layer.
Because of the nature of the MAC protocol, it is no exact
analytical method for converting a PHY rate to a UDP rate.
The UDP rate will vary with interference and radio quality
and we therefore chose to measure Rc on the UDP layer as an
input to the analytical expressions. The value of Rc was
defined to be the highest error-free bitrate and the
measurements showed Rc= 7.3 Mbit/s in areas with limited
interference, i.e. in the countryside with few houses nearby.
Since no exact measurements of Rn could be performed, we
chose to set Rc=Rn.
In order to evaluate the UDP throughput performance in
the chain of six MAPs, traffic was sent from the gateway to
Figure 6. Received UDP throughput as a function of the UDP traffic sent
from the gateway to the STA belonging to each MAP.
Fig. 7 shows the same measurements as in Fig. 6 together
with measurements performed in an area with networkexternal interference, i.e. close to a major office building
where many IEEE 802.11 networks could be observed. The
plotted UDP throughput values are the highest measured
error-free throughput that was measure for each STA. It can
be observed that the measured throughput in areas with
limited interference corresponds well with the results found
from the analytical expressions. However, in this plot the
analytical results do not take frequency re-use into account.
This may explain why the measured throughput in an area
with limited interference flatten out after the fourth MAP
while the analytical results still show a drop in the
throughput after the fourth MAP. For areas with interference,
the measured throughput is significantly lower than the
analytical results.
Figure 7. Highest error-free UDP throughput received by each of the STAs
belonging to a MAP when traffic was sent to one STA at a time.
Fig. 8 shows the UDP throughput measurements when the
traffic was sent to one or more STAs at a time, i.e. first
traffic was sent to the STA belonging to MAP1, second
traffic was sent to the STAs belonging to MAP1 and MAP2
simultaneously, then traffic was sent to the STAs belonging
to MAP1, MAP2 and MAP3 simultaneously, and so on.
These results also show that our analytical expressions can
closely predict the throughput in relatively interference-free
areas.
Figure 10. Highest error-free UDP throughput received by each of the STAs
belonging to a MAP when traffic was sent to more STAs simultaneously.
VII.
Figure 8. Highest error-free UDP throughput received by each of the STAs
belonging to a MAP when traffic was sent to more STAs simultaneously.
B. Measurements in a Network Based on IEEE 802.11g
The second set of measurements was performed for a
chain of three MAPs where the bitrate at the PHY layer
between two MAPs were fixed to 11 Mbit/s. Based on the
previous measurements we set Rn= 7.3 Mbit/s. For these
measurements the STAs communicated via IEEE 802.11g
PCMCIA cards. The highest error-free UDP bitrate between
a STA and a MAP in an area with limited interference was
measured to be Rc= 16 Mbit/s.
Fig. 9 shows the plot of the UDP throughput when traffic
was sent from the gateway to the STAs, one at a time. These
measurements also show that the analytical results can
closely approximate the throughput in an area with limited
interference.
In this paper we have investigated the throughput of IEEE
802.11-based mesh networks both through analysis and
measurements. The results show that our analytical
framework can closely predict the throughput in a mesh
network that is not exposed to interference.
VIII.
REFERENCES
[1]
[2]
[4]
[5]
Fig. 10 shows the corresponding plot for the
measurements where the traffic was sent to one or more
STAs simultaneously. First, the traffic was sent to the STA
belonging to MAP1, then the traffic was sent to the STAs
belonging to MAP1 and MAP2 simultaneously. Last, traffic
was sent to MAP1, MAP2 and MAP3 simultaneously.
FUTURE WORK
More measurements will be performed for other network
topologies and for multi-frequency WMNs in order to further
verify the applicability of the analytical framework presented
in this paper. Although our results show that the throughput
can be predicted for mesh networks operating in areas with
limited interference, in-depth investigations of the influence
of interference will be performed to be able to improve the
prediction of the throughput of real-life mesh networks.
[3]
Figure 9. Highest error-free UDP throughput received by each of the STAs
belonging to a MAP when traffic was sent to one STA at a time.
CONCLUSIONS
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