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Epidemic Algorithms
by
David Kjerrumgaard
Introduction
• A new class of networked systems is
emerging that involve very large numbers
of small, low-powered, wireless devices.
• The sheer number of devices involved in
such networks as well as the resource
constraints of the nodes in terms of
energy, storage, and processing
necessitate the development of extremely
simple algorithms for discovery, routing,
multicast, and aggregation.
• While these algorithms are easy to build,
they often exhibit complex and unexpected
behavior when they are utilized in real
world scenarios; making them difficult to
simulate accurately.
• In their paper, Ganesan et. al., provide a
wealth of detailed empirical data from a
network involving over 150 such nodes.
• This data is intended to serve as the basis
for algorithm design in the wireless space.
• Instrumentation in the experiment focused
on various levels of the protocol stack in
an effort to isolate the various factors
influencing the global behavior of the
system.
• At the Physical / Link Layer, they measured
– Packet Loss
– Effective Communication Range
– Link Asymmetry
• At the MAC Layer, they captured
– Contentions
– Collisions
– Latency
• At the Network / Application Layer
the structure of the trees
constructed was analyzed.
Epidemic Algorithms
• Refers to network protocols that
allow rapid dissemination of
information from a source through
purely local interactions.
• Messages initiated from the source
are rebroadcast by neighboring
nodes, extending outward hop by
hop until the entire network is
reached.
• The following logic depicts the schema for
message handling in a generalized epidemic
protocol:
Let S be local state of node and R a random number.
If message Mi, is received for the first time, then
Take local action based on Mi : S  f1(Mi,S).
Compose message Mi’ = f2(Mi,S).
Make Boolean retransmit decision D = f3(S,R).
if D is true, then
Transmit Mi’ to all neighbors.
• Flooding, in which the nodes always
retransmit the message upon reception is
the simplest example of an epidemic
algorithm.
• More sophisticated forms of flooding
algorithms exist, including probabilistic,
counter-based, distance-based, and
cluster-based techniques that seek to
minimize the amount of redundant packet
transmissions.
• This study employed a simple retransmit
flooding protocol, which under ideal
conditions would ripple outward uniformly
from the the source.
• When a node first receives the message, it
immediately rebroadcasts once, and
squelches further retransmissions.
Message Flooding
Flooding Anomalies
• Several indications of non-uniform flood
propagation were observed during this study
including:
• Backward Links: Links formed between nodes that
extend backward geographically toward the source.
• Stragglers: Nodes that missed the message entirely
even though neighboring nodes did receive the
message.
• Long Links: Links that were formed when the
message was received over a larger distance, usually
exceeding many hops.
• Clustering: Most nodes in the tree had few
decedents, while a few nodes had many.
Backward Link
Long Link
Straggler
Clustering
Related Work
• Prior experimental studies in this
area have tended to focus on routing
in wireless Ad Hoc networks without
addressing scaling due to a lack of
infrastructure.
• These studies were comprised of
fewer than a dozen nodes and
therefore did not address issues of
scale.
• The other tool used in analyzing the
behavior of routing protocols in
large-scale multi-hop wireless
networks is simulation.
• The results of such studies were
discounted due in large part to the
difficulty in simulating physical a
link layer characteristics in a
accurate fashion.
• Ultimately, a protocol’s performance
must be validated in the real world.
Experimental Platform
• The study employed over 175 identically
configured Rene motes equipped with:
–
–
–
–
–
–
4 MHz Amtel processor
8 Kb of programming memory
512B of data memory
916 MHz single-channel, low-power radio
10 Kbps of raw bandwidth
Uniform antenna length & orientation (both
unspecified)
– TinyOS as the runtime system
– Fresh AA batteries
• Each node uses a variation of the
Carrier Sense Multiple Access
(CSMA) protocol with a random
backoff duration between 6ms and
100ms
• During the backoff period, the radio
is powered off in order to conserve
energy, effectively blocking all
communication during this time.
• The MAC protocol keeps trying to
deliver packets until a clear channel
is found. (No dropped packets)
Testing Methodology
 Two separate sets of experiments were
conducted for this study. The first set
focused on the characteristics of links
among all nodes in a large test bed,
while the second set focused on the
dynamics of the flooding.
Experiment # 1
 169 nodes were arranged in a 13x13 grid
on an open parking structure, with a grid
spacing of 2 feet.
 The goal of this experiment was to map
the connectivity characteristics between
all nodes at 16 different radio transmit
power settings between 60 W and 72 W.
 The base station periodically issued
commands to all nodes to control the
experiment, this ensured that only one node
would transmit at a time thereby eliminating
the possibility of collisions.
 The receiving nodes transmitted in sequence
in response to the commands sent by the
base station.
 At each power setting, each node was
instructed to transmit 20 packets, 100 ms
apart. Thus, a total of 54,000 ( 16 x 20 x 169 )
messages were sent during the four hour test.
 Upon receipt of a message, the following
information was extracted from the packet
and logged in the receiver’s data memory:
 Transmitter ID ( 1 – 169 )
 Sequence number of the message ( 1- 54000 )
 Transmit power setting ( 60 – 72 )
Analysis of Experiment # 1
 The analysis from the first set of experimental
data focused on the physical and link layers.
 The goals of the analysis were:
 Explore packet loss statistics over distance.
 Attempt to quantitatively define and measure the
effective communication radius at each transmit
power setting in a real-world scenario.
 Establish a definition of what constitutes a bidirectional link and an asymmetric link, and
measure the effects of each link type on
communication.
Packet Loss Statistics
 For this study, packets that fail to pass CRC
checking are considered lost.
 During the analysis they discovered that the
distribution of packet loss over distance was nonuniform. This observation is in stark contrast to the
uniform, simple binary relation on distance used in
large-scale simulation studies, which model signal
propagation using the function 1/r where  > 2.
 The expected packet loss distribution:
The observed packet loss distribution
Radio Range
 Often described in terms of signal strength,
however from an algorithmic standpoint,
successful communication is what matters.
 During the analysis they discovered that the
decay of packet loss with respect to
distance does not experience the polynomial
falloff expected based on the signal
propagation function 1/r where  > 2. This
was especially true at larger transmit power
settings.
 During the analysis they discovered that
the throughput never reached 100%, even
at short distances from the transmitter.
They attributed this phenomenon to two
factors:
 Increased fading rate due to deployment on
the ground.
 Insufficient signal processing and forward
error correction due to the limited
computational and energy resources available
on this computing platform.
Measuring the Connectivity
Radius
 Conceptually, the connectivity radius is
thought of in terms of a circular cell. This
approach simplifies algorithm analysis
and allows a geometric approach.
 We have already seen that this
conceptualization does not fit the
empirical data collected from this study.
However, packet loss does decrease
monotonically with distance.
 The definition of connectivity radius is typically based
on a packet loss threshold, which, in turn, is based on
the ratio of “good links” to “bad links”
 Good Links: Those communication links in which we can use
forward error correction (FEC) and other techniques to
improve the raw packet throughput to adequate levels. The
packet reception probability of such a link is typically above
65%.
 Bad Links : Those communication links in which we the use
of forward error correction (FEC) and other techniques
cannot be employed to boost the throughput to acceptable
levels. The packet reception probability of such a link is
typically below 25%.
 Given the previous definitions, we can
define the connectivity radius of a node N
to be the radius R of the smallest circle
that encompasses 75% of the nodes
having a good link with N.
• During the analysis they observed a linear
variation of the connectivity radius with
the transmit power setting on the mote.
Measure the Effects of Asymmetric
and Bi-directional Links on
Communication
 Asymmetric Links: Those communication
links that are “good” in one direction and
“bad” in the other.
 Bi-directional Links: Those
communication links that are “good” in
both directions.
 While asymmetric links arise
relatively infrequently in spare
wireless networks, they are very
common within a field of low-power
wireless nodes.
• The distribution of asymmetric links
over the entire test network is shown
below.
 The analysis of the data collected during the first
experiment reveals that for the range of transmit
power settings studied, approximately 5-15% of
all links are asymmetric with the percentage
increasing inversely with the power setting.
 At short distances from the transmitter, a
negligible percentage of links are asymmetric, but
this percentage grows significantly with
increasing distance, especially at lower power
settings.
 The distribution of bi-directional and asymmetric
links over distance is shown below:
Experiment # 2
 156 nodes were arranged in a 13x12 grid on
an open parking structure, with a grid
spacing of 2 feet.
 The base station was placed in the middle of
the base of the grid and initiated flooding
periodically, with each period lasting long
enough to allow the flood to settle down.
 Each receiving node rebroadcast the
message immediately upon receipt of the
flood message and then squelches all
further broadcasts.
 Eight different transmit power settings were
studied and 10 non-overlapping floods were
issued at each of these settings.
 Upon receipt of a message, the following
information was extracted from the packet and
logged in the receiver’s data memory:
 Transmitter ID ( 1 – 156 ), which was used to reconstruct
the propagation tree.
 Two locally generated timestamps, each with a
granularity of 16 s.
 The first timestamp recorded the total amount of time
that a message was stored on a node before being
retransmitted.
 The second timestamp recorded the interval for which
the node was in backoff mode.
Analysis of Experiment # 2
 The analysis from the second set of
experimental data focused on the MAC
and application layers.
 The goals of the analysis were:
 Capture different aspects of the message
propagation including; maximum backoff
interval, reception latency, settling time,
useless broadcasts, and collisions.
 Analyze the routing tree construction of the
epidemic algorithm.
Medium Access Layer Analysis
 Maximum Backoff Interval
 A metric that captures the contention level within an
interference cell, is the maximum backoff interval, which
reflects the time till contention subsides in each cell.
 The distribution of backoff intervals in the network indicates
the extent of contention that each node perceives in the
channel.
 As transmit power increases, contention grows as a result of
interference cell growth.
• As contention increases, nodes are forced to backoff
for increasingly longer intervals as shown below:
 During the analysis they observed
that the transmit power setting and
the 95% backoff interval threshold
were directly proportional to one
another.
 Insert Table 3 here
Reception Latency
 Defined to be the total amount of time required by
nodes in the network to receive an epidemic
broadcast packet.
 As expected, for higher transmit power settings the
reception latency decreased proportionally with the
network diameter.
• An interesting observation is that a significant
fraction of the total propagation time was taken to
reach the last few nodes in each plot.
 The following figure shows the relationship between
the reception latency and the network diameter, which
refers to the maximum number of hops from the
source to any node in the network.
Settling Time
 Defined to be the time taken for delivery of
a single packet flood throughout the entire
network, and is equivalent to the reception
latency plus the maximum backoff
interval.
 The settling time is bounded as shown
below:
Max( MaxBackoffInterval, Reception Latency)
Settling Time
 MaxBackoffInterval + Reception Latency

 At low transmit power settings, the settling time is
closer to the reception latency than the maximum
backoff interval. This suggests that the flood
propagation delay has a more significant impact
than the time taken for broadcasts to subside
within the interference cells.
 As the transmit power is increased, the settling
time moves closer to the maximum backoff
interval, suggesting that contention within each
interference cell becomes the dominate factor.
• The relationship between settling time and
reception latency is shown in the following
diagrams.
Useless Broadcasts
 Defined to be the percentage of rebroadcasts that
deliver a message only to nodes that have
already received one. Typical causes for such
broadcasts include:
 All neighbors have already received the message
 The rebroadcast suffers packet loss or collision
 Analysis of the experimental data revealed that at
higher transmit power settings, nodes in the
network keep retransmitting the message long
after 95% of the nodes already received it.
 Conversely, the lowest transmit power setting
examined had only a 60% useless broadcast rate.
Collisions
 During the analysis they observed that for all power settings,
the time required for all nodes to receive the flood is nearly
identical.
 At very high transmit power, the last 5% of the nodes take as
much time to receive their packets as the first 95%. This
phenomenon can be attributed to stragglers and backward
links.
 In broadcast-style epidemic transmission, a packet does not
have an intended recipient, so CSMA without RTS/CTS is used.
However, we are able to combine the global ordering the packet
transmissions and link layer estimates of the communication
cell to infer the impact of collisions.
 The following charts show the relation between the number of
colliding transmitters, stragglers, and backward links.
 Timestamps generated at the MAC level were used to
estimate the number of colliding nodes. Using the
connectivity radius established in the first experiment
allowed them to detect intersecting communication
cells for each set of colliding transmitters.
 This provides an estimate for the number of nodes
that should receive the packet, but do not as a result
of collisions.
 Collisions result in the creation of stragglers , which
miss the propagation in the early stage of the flood
and eventually form backward links from a later
reception.
 At higher transmit power settings, communication
cells grow, resulting in a larger number of stragglers,
and consequently backward links.
Network and Application Layer
Analysis
 The reverse routing tree was constructed from
the information collected at the Network layer
during the experiment. Analysis of the reverse
routing tree has greater relevance in the
majority of algorithms developed for this
computing platform, such as:
 Data gathering applications
 Reactive mobile ad hoc routing algorithms with
caching
 Multicast algorithms
 Link Layer analysis has shown that long
links have a greater potential for asymmetry
and therefore are less appropriate for use
as the reverse path to draw data back to the
source.
 Similarly, backward links in the tree are
sub-optimal since data flows away from the
base station rather than towards it on the
reverse path.
 The following figure depicts the various
factors affecting tree structures
 The parent selection mechanism has a large role in influencing
the tree structure. In fact, the opportunistic, earliest-first parent
selection mechanism used in this study resulted in highly
clustered trees, with most nodes being leaves and only a small
number of parent nodes, each with a large number of children.
 Large clusters were observed across all eight of the transmit
power settings being studied and this behavior was
exacerbated by the presence of long links for the following
reason;
 Nodes at the end of long links have a greater probability of seeing
less interference and typically have many neighbors who have not
received the flood packet.
 Consequently, these nodes retransmit the packet faster due to an
absence of any backoff interval, and reach more uncovered nodes,
resulting in the highly clustered behavior observed in the study.
Key Observations &
Recommendations
 Much of the literature has assumed a circular disc model for
the cell regions. The data gathered in this study implies that
a probabilistic view of modeling is a more realistic approach.
 The fact that asymmetry manifests itself more on long links
is significant to many ad-hoc routing protocols that use
shortest reverse hop-count as a method for setting up
routing paths. These protocols naturally select links that are
long in nature, thereby increasing the probability of selecting
a poor reverse end-to-end route.
 The empirical data from this study suggests that asymmetric
links are indeed likely to be significant in large scale,
multihop networks and robust protocol must deal
appropriately with asymmetric links through mechanisms
such as filtering.
 Reducing the transmission power in an epidemic
broadcast reduces the number of useless
broadcasts. Therefore, energy can be conserved by
reducing the transmit power setting.
 Rebroadcasts that are transmitted after a large
backoff delay relative to the elapsed time are likely to
be useless. Therefore, dropping these rebroadcasts if
tight estimates of the reception latency are available
to nodes can save energy.
 In order to maximize throughput, it is useful to
pipeline transmissions from the base-station, such
that two successive transmissions are separated by
the amount of time it takes to propagate two
transmission cells.
 Settling time gives a lower bound on achievable
multicast throughput, of 1 / Settling time.
Implications on Algorithm
Design
 Simple protocols with very few states can exhibit
unanticipated global complexity due to their
interaction with the complex physical world.
 Algorithm designs should use a probabilistic
abstraction to model connectivity
 Asymmetry is to be expected, and certain protocol
choices may exacerbate this effect. Robustness to
asymmetry is a crucial part of protocol design in these
systems.