A Model for the Loss of Hello-Messages in a
Wireless Mesh Network
Geir Egeland
Department of Electrical and Computer Engineering
University of Stavanger, Norway
Email:geir.egeland@gmail.com
Abstract—The links in an ad hoc or wireless mesh network are
normally kept alive by the exchange of Hello-messages between
neighbouring nodes. These Hello-messages are prone to collisions
with traffic from hidden nodes. If several Hello-messages are lost
due to overlapping transmissions, the node expecting the Hellomessages erroneously assumes that the link is down. This is called
an apparent link-failure. This paper provides an analytical model
for the loss of Hello-messages in a mesh network. Knowing the
probability of losing a Hello-message, the probability of apparent
link-failures can easily be found, which can further be used in
reliability analysis of wireless mesh networks.
I. I NTRODUCTION
The performance of an ad hoc network, such as a wireless mesh network, depends strongly on the routing protocol’s ability to preserve links between neighbouring nodes.
A common method is to establish and maintain the links
proactively by the use of one-hop Hello-messages, which are
exchanged between neighbouring nodes. Regardless of the use
of link maintenance schemes, link-failures will be present in
ad hoc networks. Some link-failures are unavoidable, such
as when a wireless node deliberately leaves a network or
is subject to a power failure. Also, a link will cease to be
operative when two nodes move out of each others radio
transmission range. In addition to these, a set of link-failures
which are referred to as apparent link-failures exist. They
are primarily caused by loss of Hello-messages as a result
of overlapping transmissions from hidden nodes [1]. The
performance degradation can be significant in wireless mesh
networks, and a model for apparent link-failures is needed in
order to find ways to prevent them and improve the network
reliability. This is the main motivation of this paper, where an
analytical model for loss of Hello-messages is presented.
Hello-messages are broadcasted in order to conserve network resources. Thus, every link on which a Hello-message
is received effectively obtains maintenance from only one
message. Broadcast packets are not acknowledged, and Hellomessages are therefore inherently unreliable. A node anticipates to receive a Hello-message from a neighbour node within
a given time interval and can accept that messages occasionally
will be missing due to various error conditions. However,
if a node fails to receive a number (r + 1) of consecutive
Hello-messages, it will assume that the node on the other side
of the link is permanently unavailable and that the link is
Paal E. Engelstad
University of Oslo, Simula and
Telenor GBD&R, Norway
Email:paal.engelstad@telenor.com
inoperable. The value of the configurable parameter r is a
tradeoff between providing the routing protocol with stable and
reliability links (a large r), and the ability to detect link failures
in a timely and fast manner (a small r). Since Hello-messages
are broadcasted, they are unable to take advantage of the
Request-To-Send/Clear-To-Send (RTS/CTS) signalling, which
adds protection against hidden nodes for the IEEE 802.11
MAC protocol’s [2] unicast data transmissions. Although some
Hello-message loss is avoided using RTS/CTS, it will only
help the links of the node that issues the CTS. The result is
that the Hello-messages will be susceptible to collisions with
traffic from hidden nodes even if RTS/CTS is enabled. Thus,
the utilisation of a link may be prevented since the link can be
marked as inoperable due to Hello-message loss. An example
of a routing protocol that makes use of Hello-messages is the
proactive protocol Optimized Link State Routing (OLSR) [3].
Reactive routing protocols can also maintain links proactively
using Hello-messages. Indeed, this is an optional mode of
operation for the reactive Ad hoc On-Demand Distance Vector
(AODV) routing protocol [4].
Not much published work relates directly to modelling of
the loss of Hello-messages in wireless mesh networks. In [5]
the performance of neighbour sensing in ad hoc networks
is studied, but only parameters such as the transmission
frequency of the Hello-messages and the link-layer feedback
are covered. In [6] a model for packet collision and the
effect of hidden and masked nodes are studied, but only for
simple topologies, and the work is not directly applicable
to the Hello-message problem. The work in [7] addresses
link-failures in wireless ad hoc networks through the effect
of routing instability. Here the authors study the throughput
of TCP/UDP in networks where the routing protocol falsely
assumes a link is inoperable. However, what causes a link to
become unavailable to the routing protocol is not studied.
The main contribution of this paper is an analytical model
for the probability of losing Hello-messages caused by overlapping transmissions from hidden nodes. The model provides
upper and lower bounds and can serve as input to link
reliability analysis. The validity of the model is supported
by simulations. Further, two example topologies are studied
where we show that the probability of losing Hello-messages
caused by overlapping transmissions can be significant. For
simplicity, we refer to these Hello-messages as beacons in
the analysis. From the model, we find the probability (perror )
that one such beacon is lost as a result of a packet collision,
notably a collision with a transmission from hidden nodes.
The probability that a receiving node considers a link to be
inoperative at the time a beacon is expected, can then typically
be found as pr+1
error .
The rest of the paper is organised as follows: Section II
presents the network and the analytical model. This section
also verifies the analytical model. The model is then compared
with simulation results from the ns-2 network simulator [8] in
section III, where the beacon loss in arbitrary mesh topologies
also is analysed. Finally, conclusions are drawn in section IV.
II. A M ODEL FOR B EACON L OSS P ROBABILITY
A. Assumptions and example topologies
In order to simplify the analysis, the model is based on a
set of assumptions. First, it is assumed that a beacon sent by
a node has a negligible probability of colliding with a beacon
from any of the neighbouring nodes. This is a fair assumption,
since beacons are short packets that are transmitted periodically and at a random instant at a relatively low rate. Second,
it is assumed that the probability that the beacon collides with
a data transmission from any of the (non-hidden) neighbouring
nodes also is negligible. This is a relatively fair assumption,
since a MAC layer often has mechanisms that reduce such
collisions to a minimum. Examples of such mechanisms are
the collision avoidance scheme of the IEEE 802.11 MAC
protocol, with randomised access to the channel after a busy
period, and the carrier- and virtual sense of the physical layer.
Thus, the probability that beacons are lost, is the result of
overlapping data packet transmissions from hidden nodes only.
The two example topologies that are illustrated in Figure 1
will serve as reference for the explanation of the model. In
the two topologies, node s0 transmits beacon packets to its
neighbouring nodes (node s1 ). However, node s1 has three
neighbour nodes that are hidden from node s0 . Thus, if any
of the nodes in the set {s2 , s4 , s6 } have data (D) to transmit,
this might overlap with the beacons (B) from node s0 , and
overlap/collide at node s1 . In Figure 1(a) the hidden nodes are
not within the radio transmission range of each other, while in
Figure 1(b) they are all within each others range. These two
examples represent two extremes, forming upper and lower
bounds on the performance of a real system.
The data traffic from the nodes in the set {s2 , s4 , s6 } is
modelled as an M/M/1 queue where the data rate is Poisson
distributed with parameter λc and the channel access and
transmission time is exponential distributed with parameter
1/µ. This is not very realistic, since traffic in a real network
will follow other distributions. However, it allows us to verify
the model in a simple manner. Later in the paper we will
provide upper and lower bounds for the beacon loss probability
that is based on a large number of random independent traffic
scenarios, which captures more of the characteristics of the
traffic in a real network.
D
s2
s0
B
s1
D
s6
s4
s3
D
D
s2
s7
s0
s5
(a) Isolated hidden nodes
B
s1
s6
s4
s3
D
D
s7
s5
(b) Connected hidden nodes
Figure 1. Sample topologies where the hidden nodes {s2 , s4 , s6 } are isolated
or connected. When the hidden nodes send data (D), this may collide with
the beacons (B) sent by node s0 .
B. Beacon collision with only one hidden node
Consider the topology in Figure 1(a). We want to find
the probability (perror ) that the beacon from s1 and a data
packet from the hidden node s2 collide. If qs2 (0) denotes
the probability of node s2 having zero packets awaiting in
its buffer, perror is expressed as [9]:
perror = Pr{Collision|qs2 (0) > 0} · Pr{qs2 (0) > 0}
+ Pr{Collision|qs2 (0) = 0} · Pr{qs2 (0) = 0}
= (1 − p0 ) · 1 + (1 − e−λc ωb /Tp ) · p0
(1)
where p0 is the probability that the hidden node s2 has
zero packets awaiting to be transmitted. The parameters Tp
and ωb represent the average transmission time of the data
packet and of the beacon packet, respectively. Both these
transmission times are assumed to be exponentially distributed.
The probability that a node has i data packets in its packet
queue is given by pi = (1 − ρ)ρi , where ρ = λc /µ, thus
p0 = 1 − ρ [10].
C. Isolated hidden nodes
We will now evaluate the probability that a beacon collides
with data transmissions from a set of hidden nodes using the
topology illustrated in Figure 1(a). In this example topology,
the hidden nodes are assumed to be isolated, i.e. outside the
transmission range of each other. Individually, the probability
that one of them sends a data packet which overlaps with
a beacon from node s0 is given by Eq. 1 (denoted pe ).
The number of data packets overlapping with a beacon is
binomially distributed B(m, pe ) where m is the number of
hidden nodes. The probability that a beacon is lost can then
be expressed as:
m X
m k
pIerror (m hidden nodes) =
p (1 − pe )m−k (2)
k e
k=1
D. Connected hidden nodes
In Figure 1(b) the hidden nodes are all within radio transmission range of each other. When all the hidden nodes are
connected, the calculation of the beacon loss probability is not
as straightforward, and we need to make some simplifying
assumptions. First, it is assumed that the nodes access the
common channel according to a 1-persistent CSMA protocol
[11]. This might seem like a contradiction, since it was
stated earlier that we assumed a MAC protocol that reduces
the collisions between non-hidden neighbours to a minimum.
However, for the case where the hidden nodes are connected,
mλc
x0
mλc
x1
µz1
mλc
µz2
mλc
mλc
···
x2
µz3
xN −1
µzN −1
xN
µzN
Figure 2. A Markov model of the total number of packets waiting to be
transmitted by the m hidden nodes where λc is the mean packet arrival rate,
1/µ is the mean service time and zn is the average number of the m hidden
nodes transmitting simultaneously.
there will be a parameter (zn ) in the model that can be set
to control to which extent transmissions between the hidden
nodes are permitted to collide with each other. Second, it is
assumed that the arrival rates at the different hidden nodes
are not coupled, hence a Markov model can be used for the
analysis.
Consider the Markov chain illustrated in Figure 2. Each
state represents the sum of all packets queuing up in the m
hidden nodes. Here zn is the average number of hidden nodes
transmitting when a total of n packets are distributed amongst
the hidden nodes.
We now want to find the probability of being in state x0 ,
which is the case for which none of the hidden nodes have
packets awaiting transmission (pC
0 ). Using standard queuing
theory [10], it can easily be shown that this probability is
given by:

!−1 −1
N
i
X
Y

 , ρ = λc
(3)
pC
(mρ)i
zn,i
0 = 1+
µ
n=1
i=1
where zn,i is the average number of the m nodes transmitting
simultaneously and is calculated according to:

i=1
1


Pn

m

k(m
β
(1−ρ
)
)
k,n

n<m,i>1

Pn k m
 k=1
ρ=λc /µ
( )βk,n
k=1 k
(4)
zn,i =


 Pm−1 m


(1−ρm )
k( )β
n≥m,i>1

Pm−1k mk,n
 k=1
+m·ρm
ρ=λc /µ
β
( k ) k,n
k=1
The probability that one or more of the m nodes having zero
packets in its buffer, given the sum of packets in the buffers is
n, is given by the term 1 − ρm in Eq. 4. The combinations of
k of m buffers containing packets,
constrained by a total sum
of n packets is given by m
β
,
where βk,n is calculated
k,n
k
using:

k=1
1




n − 1
k=2


n−2−
P
n− n−(k−2)−
k−1
βk,n =
ij

ik−1
(k−1)
j=3

X
X
X

Pk−1


··
n − 1 − j=2 ij k>2


ik−1 =1
ik−2 =1
i2 =1
By substituting p0 in Eq. 1 with pC
0 (Eq. 3), the probability
that transmissions from the connected hidden nodes overlap
with a beacon can be calculated as:
C
−λc ωb /Tp
pC
error = 1 − p0 · e
(5)
(a) Results for Figure 1(a)
(b) Results for Figure 1(b)
Figure 3. The probability of beacon loss (ωb /Tp = 0.3) for the topologies
illustrated in Figure 1. The results are shown with a 95% confidence interval.
In order to test the model’s accuracy, a discrete-event simulator was developed. The simulator models a two-dimensional
network where every node transmits with the same power
on the same channel. Also, every node experiences the same
path loss versus distance and have the same antenna gain and
receiver sensitivity. A node receives a packet if and only if the
packet does not overlap with any other packet transmitted by
a node within its range. The propagation delay is assumed to
be negligible and the nodes are static. The correctness of the
simulator was verified using mathematical expressions for the
Aloha [12] and p-persistent CSMA [11] protocol, where MAC
layer throughput was compared with the simulation results.
Figure 3 shows the probability of overlapping transmissions
for the topologies in Figure 1. Analytical and simulated results
are shown. Packets at each node were generated independently
according to a Poisson process with the average rate λc . The
results in Figure 3 show that the model provides sufficient
accuracy, even though the model assumes that the length of
a packet from a hidden node is exponential distributed, while
the simulation model uses a fixed packet length. This indicates
that our simplification is fair and that the model provides
satisfactory accuracy.
E. Bounds for the beacon loss probability
The beacon loss probability depends on how the hidden
nodes of s1 access the channel and if they have packets
in their buffer. For the case where the hidden nodes are
isolated, any packet that arrives at one of these nodes will
be transmitted immediately, since they will never sense the
channel as busy. This will represent a lower bound for the
beacon loss probability.
When the hidden nodes are connected, i.e. within each
others transmission range, a packet arriving at one of the
hidden nodes might have to wait until an ongoing transmission
is finished before it is transmitted. When all the buffers are
filled, the m hidden nodes will transmit simultaneously after
an ongoing transmission is finished, thus emptying the buffers
at a rate of m · µ. If we however change the model for the
connected case, and enforce that the hidden nodes access the
d6
d10
d6
d10
d4
d8
d12
d4
D
d2
D
d7
d9
d11
d0
d1
D
d3
d5
(a) Topology A
Figure 4. The probability of beacon loss (ωb /Tp = 0.3) for the topology
illustrated in Figure 1. Upper and lower bounds are calculated using Eq. 3
(connected hidden nodes and zn = 1∀n), and Eq. 2 (isolated hidden nodes),
respectively. The case where zn is calculated according to Eq. 4 is also shown.
channel one at a time, the rate of emptying the buffers of the
hidden nodes is reduced to µ, and can be calculated using
Eq. 3 with zn = 1∀n. The model will now resemble the
IEEE 802.11 MAC protocol, which has mechanisms that aim
to reduce collisions on the channel to a minimum. This will
represent an upper bound for the beacon loss probability.
Figure 4 illustrates the upper and lower bounds for the
probability of overlapping transmissions for the topologies in
Figure 1. An interesting result is that when using a MAC
mechanism that reduces the probability of unicast packet
collisions on the channel, the probability of beacon loss is
increased. The reason is that the data packets of the hidden
nodes then ”fills up” the channel more efficiently, leaving less
residual time for a beacon to be transmitted on the channel
without colliding with a data packet.
III. B EACON L OSS IN A RBITRARY M ESH T OPOLOGIES
A. Analysis of some selected traffic patterns
Up to this point, the analysis has only considered the basic
topologies in Figure 1. In this section we investigate how the
analysis of these topologies can be applied to more complex
mesh topologies and focus the study on the two topologies
in Figure 5. We can observe that the analysis can easily be
generalised for any arbitrary mesh topology. First, we study a
specific traffic pattern as shown in Figure 5. Then, in the next
sub-sections, the beacon loss probability for random traffic
patterns will be analysed.
In order to see how the model performs in a realistic
situation, the self-developed discrete-event simulator used in
previous section is abandoned. Instead, we now compare the
analysis with results from the ns-2 network simulator, using
the IEEE 802.11 MAC protocol in the simulations. Table I
shows the simulation parameters. The ns-2 model is configured
such that the sensing range (CP) is equal to the transmission
range (RX). The traffic is generated according to a Poisson
process where the packet size is fixed. It is expected that the
results for the probability of beacon loss might differ, since
MAC layer
Slot time
Values
20µs
d0
d7
B
d9
d1
d11
d3
d5
(b) Topology B
Figure 5.
NS -2
d8
d2
D
B
D
The simulation topologies.
Table I
S IMULATION PARAMETERS .
Physical layer
Propagation
model
SIFS/DIFS
10/50µs CPThreshold
Queue Length 50
CS/RXThreshold
RTS-CTS
OFF
Data rate
Values
Simulation
Two Ray Simulation/
transient time
10 dB
Traffic/
Distribution
Equal
Packet size
(UDP/IP/MAC)
11.0Mbps #Replications
Values
900s/25s
Poisson
1478
10
the CSMA protocol in the analytical model is different from
the IEEE 802.11 MAC protocol used in the ns-2 simulator.
In addition, effects such as retransmission by the MAC layer
in the ns-2 simulator will cause the packet buffers to be
emptied differently than in an M/M/1 queue. However, the
traffic pattern chosen in Figure 5 is such that probability of
MAC retransmissions is negligible.
Figure 6 shows the beacon loss probability for the topologies in Figure 5. The maximum traffic load per node in the
ns2-simulation is 2Mbps ≈ 0.27(λc T ). The results in Figure
6 show simulated and analytical beacon loss probability. The
parameters Tp and ωb in Eq. 1 is calculated according to [13]
and the parameters in Table I.
In topology A, node d1 has two hidden nodes and these
two nodes transmit data to one of their 1-hop neighbours
(d7 →d8 and d3 →d5 ). The beacon is sent from d0 →d1 and
ωb is calculated to be 1104µs. The traffic/topology scenario
is the same as in Figure 1(a) and the results are shown
in Figure 6(a). From the figure we can see that the model
provides satisfactory accuracy compared to the simulation
results from ns-2. This is as expected, since there is no data
packet loss, thus no retransmissions or any contention for
channel access in this topology. In topology B, node d7 has
three hidden nodes which transmit data to one of their 1-hop
neighbours (d0 →d1 , d2 →d4 and d8 →d10 ). The beacon is sent
from d9 →d7 and ωb is calculated to 1392µs. The analytical 1persistent CSMA model was modified in order to resemble the
results from the ns-2 simulation. By setting zn = 1∀n in Eq.
3, we imitate the channel access behaviour of the IEEE 802.11
MAC protocol, where the probability of a collision between
transmissions of the connected hidden nodes is minimal. The
results in Figure 6(b) show the beacon loss probability for
topology B. We observe that the simulation result also in this
scenario matches well with the analytical model.
(a) Results for topology A
(b) Results for topology B
Figure 6. The probability of beacon loss for the topology illustrated in Figure
5. The results are shown with a 95% confidence interval.
B. Complex traffic patterns
Before attempting to model more complex traffic patterns,
we must ensure that the basic model is capturing all possible
transmission configurations. In fact, the initial model did not
take into account the possibility that a neighbouring node
receiving the beacon could be transmitting any data packets.
Therefore, an approximate model will be provided, where the
channel access time of the neighbouring node receiving the
beacon is also taken into account. This model will be used in
the next sub-section when random traffic patterns is analysed.
Again, consider the sample topology illustrated in Figure
1(a). Let us assume that node s1 has a traffic load with the
rate λc and the probability that it gains access to the channel in
order to transmit a packet is ps1 . If the nodes {s1 , s2 , s4 , s6 }
are modelled as M/M/1 queues, the probability that e.g. node
s2 has no packets in its buffer can be expressed as:
"
k #−1
N X
ρ
qs2 (0) = 1 +
, ρ = λc /µ (6)
1 − ps1
k=1
An approximate expression for ps1 is the probability that none
of the neighbour nodes of s1 have
Q a packet in its buffer. The
probability ps1 is then given by i∈{2,4,6} qsi (0) and can now
be written as:
"
k #−n
N X
ρ
(7)
ps1 ≈ 1 +
1 − ps1
k=1
where solutions for ps1 can be found numerically and n =
|{s2 , s4 , s6 }|. For the case of isolated hidden nodes in Figure
1(a), the parameter p0 in Eq. 1 can now be expressed as qsi (0)
in Eq. 6.
For the connected hidden nodes in Figure 1(b), the probability ps1 is equal to 1/(m + 1), since each of the m + 1
nodes gets an equal share of the common channel. Thus, pC
0
is rewritten as:


i !−1 −1
N
i
X
Y
1
C
i

(8)
p0 = 1 +
(mρ)
zn,i 1 −
m+1
n=1
i=1
(a) Results for topology A
(b) Results for topology B
Figure 7. The probability of beacon loss for the topology illustrated in
Figure 5. In topology A, the beacon is sent from d0 →d1 and data from
d7 →d8 , d3 →d5 and d7 →d9 (ωb |d0 = 1104µs). In topology B, the beacon
is sent from d9 →d7 and data from d2 →d4 , d8 →d10 , d0 →d1 and d7 →d9
(ωb |d9 = 1392µs). Maximum traffic load per node in the ns2-simulation is
2Mbps ≈ 0.27(λc T ). The results are shown with a 95% confidence interval.
Using Eq. 6-8, we can now calculate the beacon loss probability in the case where node d1 transmits data to node d0 in
Figure 5(a) (topology A), and where node d9 transmits data
packet to node d7 in Figure 5(b) (topology B). Analytical and
ns-2 simulation results are shown in Figure 7. As can be seen
from the figure, the approximation for complex traffic patterns
in the model achieves acceptable results.
C. Random traffic pattern of bursty traffic
In this section we investigate the case for where the data
traffic is bursty and the traffic pattern is random. The simplest
approach to analyse a bursty traffic pattern, is to generate
a snapshot of the traffic in the topology. It is assumed that
the time between each snapshot is sufficiently long for the
traffic patterns of each snapshot to be considered independent.
For each link in the topologies in Figure 5, we now assume
that a burst of data packets is transmitted with the probability
ptx /2. The data packets within a burst are generated according
to a Poisson process with the rate parameter λc = 0.2.
This snapshot represents a possible data transmission pattern.
Generating a large number of random independent snapshots
for a given ptx , the overall average beacon loss probability for
a given λc can be found.
The Figures 8-9 show results for Topology A and B,
respectively and illustrates that the beacon loss probability
is significant even at a relatively low load of λc T = 0.2.
The simulation results are generated using the self-developed
discrete-event simulator and show the average beacon loss
probability based on 100 random generated traffic patterns
with a 95% confidence interval. The simulation time for each
burst is 600s. The figures also show analytical results based
on the 100 random independent generated traffic patterns,
where average upper and lower bounds for the beacon loss
probability are calculated. The upper bound corresponds to
the extreme case where all hidden nodes are connected with
zn = 1∀n, while the lower bound corresponds to the other
Figure 8. Probability of beacon loss (simulated and analytical) for the topology illustrated in Figure 5(a) (topology A). Traffic flows from di → dj , i 6= j
with probability ptx at the rate λc T = 0.2.
advanced simulation tool (ns-2), it was observed that the
model provides acceptable accuracy for simple topologies.
Also, more advanced topologies with random traffic patterns
and bursty traffic have been studied, where the model manages
to provide average upper and lower bounds for the beacon loss
probability with satisfactory accuracy. As shown in this paper,
the Hello-message loss probability caused by overlapping
transmissions can be significant in wireless mesh networks.
Both in the analysis and simulations it has been assumed
that all arrival rates are decoupled. Extending the analysis to
also consider multi-hop packet flows could be an interesting
topic for further research. Also, in reliability studies of wireless mesh networks, a given link failure probability often is
assumed. The Hello-message loss probability is a key element
of a routing protocol’s link-failure detection mechanism. An
interesting topic for future work would be to extend the model
to also cover link-failure probability for beacon based linkmaintenance in wireless mesh networks, where a good model
is missing in order to determine the bounds for the link-failure
probability.
ACKNOWLEDGMENT
This work has been financed by the Research Council of
Norway through the SWACOM project.
R EFERENCES
Figure 9. Probability of beacon loss (simulated and analytical) for the topology illustrated in Figure 5(b) (topology B). Traffic flows from di → dj , i 6= j
with probability ptx at the rate λc T = 0.2.
extreme where all hidden nodes are isolated. As the results
show, the analytical upper and lower bound provide a good
indication of the expected beacon-loss probability. However,
as ptx increases it can be seen that the gap between the upper
and lower bound increases. This is a result of complex traffic
pattern and interaction between the nodes. For the case when
ptx → 1 (i.e. there is traffic on every link) and the relatively
low traffic load of λc T = 0.2, it is natural that the upper and
the lower bound differ. However, for high values of ptx and
as λc T → 1, we expect that the gap between the upper and
lower bound will be small, since the probability that any of
the hidden nodes have a packet awaiting transmission is close
to 1. The study of this is however an area for future work.
IV. C ONCLUSION AND F UTURE W ORK
This paper introduces an approximate model for the Hellomessages loss probability caused by overlapping transmissions
is wireless mesh networks. The model, which assumes a
CSMA MAC layer is further extended to provide rough upper
and lower bounds for Hello-message loss probability in IEEE
MAC. Using both a self-developed simulator and a more
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