Gossip-Based Ad
Hoc Routing
Yulin Zhu
Nov. 18, 2004
1
Contents


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
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
Introduction
Pure Gossip
Optimization of Gossip
Incorporate Gossip in AODV
Parametric Probabilistic Sensor Network
Routing
Summary
2
Ad Hoc Network

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Ad Hoc Network is a multi-hop wireless network with
no fixed infrastructure.
Applications include disaster relief, tetherless
classrooms, and battlefield.
Power supply of individual nodes is limited, wireless
bandwidth is limited, channel condition varies
greatly, and routes may constantly change for node
mobility.
Robust routing protocols must be developed. Some
variant of flooding is usually used.
3
Flooding and Gossiping

Flooding
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Every node that receives a packet retransmits the
packet to all of its neighbors.
Many routing messages are propagated
unnecessarily.
Gossip

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Each node forwards a message with some
probability.
Overhead is reduced.
4
Gossip – Bimodal Behavior
Let the gossip probability be p. Then, in
sufficiently large nice graphs, there are
fractions θS(p) and θR(p) such that the gossip
quickly dies out in 1 − θS(p) of the executions
and, in almost all of the fraction θS(p) of the
executions where the gossip does not die
out, a fraction θR(p) of the nodes get the
message. Moreover, in many cases of
interest, θR(p) is close to 1.
5
Gossip – Bimodal Behavior (cont.)


In almost all executions of the algorithm,
either hardly any nodes receive the message,
or most of them do.
By making the fraction of executions where
the gossip dies out relatively low while also
keeping the gossip probability low, we can
reduce the message overhead.
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Contents






Introduction
Pure Gossip
Optimization of Gossip
Incorporate Gossip in AODV
Parametric Probabilistic Sensor Network
Routing
Summary
7
GOSSIP1(p)


A source sends the route request with
probability 1. When a node first receives a
route request, with probability p it broadcasts
the request to its neighbors and with
probability 1 – p it discards the request; if the
node receives the same request again, it is
discarded.
Problem with initial condition of the source
having very few neighbors.
8
GOSSIP1(p, k)
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For the first k hops, we gossip with probability
1. From the hop k + 1, the gossip probability
is p.
GOSSIP1(1, 1) is equivalent to flooding.
GOSSIP1(p, 1) is equivalent to GOSSIP1(p).
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Theorem II.1
For all p ≥ 0, for almost all infinite graphs, if
GOSSIP1(p,0) is used by every node to
spread a message, then there is a welldefined probability θ0S(p) < 1 that the
message reaches infinitely many nodes.
Moreover, the probability θ0F (p) that a node
receives the message and forwards it in an
execution where the message reaches
infinitely many nodes is equal to θ0S (p).
10
Cont.
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
θ0S(p) = θ0F (p) =def θ0(p)
In an execution where the message does not
die out, the probability that a random node
receives the message is θ0(p)/p.
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For GOSSIP1(p, k)
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θkS(p) – Probability that a message reaches
infinitely many nodes.
θ1S(p) = θ0(p) / p
Given that a message doesn’t die out, the
probability that a node receives and forwards
the message is still θ0(p).
12
Bimodal Behavior
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
Either hardly any nodes get the message, or
a fraction θ0(p) / p receive the message.
In cases of interest, θ0(p) is quite close to p.
Thus, in almost all executions of the
algorithm in sufficiently large graphs, either
hardly any nodes receive the message, or
most do.
13
Experiment – Probability
varies
Gossiping on a random network of average degree 8.
The higher the probability, the higher the fraction of nodes receive
the message.
14
Experiment - Probability varies
Gossiping on a random network of average degree 8.
The higher the probability, the higher the fraction of nodes receive
the message.
15
Experiment – Degree of
network
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
In a 20 × 50 regular network of degree 6, gossiping
with probability .65 ensure that almost all nodes get
the message in almost all executions.
for a 20 × 50 regular network of degree 3, we need
to gossip with probability .86 to ensure that almost
all nodes get the message in all executions.
Conclusion: the higher the degree, the better the
gossiping effect.
16
Experiment - θkS(p) with p
A critical probability p can be chosen so that almost
all the executions don’t die out.
17
Experiment - θkS(p) and θkR(p) with k

θkR(p) = θ0(p) / p – doesn’t change with a fixed p.

θ1S(p) = θ0S(p) / p.
θ1S(.65) = .95, θ2S(.65) = .98, θ5S(.65) = 1.
θ1S(.6) = .53, θ4S(.6) = .67, θ10S(.6) = .73.


Conclusion:
- As k goes from 0 to 1, there is a significant increase of
θkS(p).
- As k increases beyond 1, there is increase in θkS(p),
but it is not significant.
18
GOSSIP1(p, k) - Conclusion
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

With p sufficiently high, we can guarantee that
almost all nodes will receive the message in almost
all executions.
Practically, we can guarantee that the destination
node receives the message, while saving a fraction
of 1 – p of messages.
In cases of interest, the probability is about .65 - .75.
All nodes get the message using 25-35% fewer
messages than flooding.
19
Contents






Introduction
Pure Gossip
Optimization of Gossip
Incorporate Gossip in AODV
Parametric Probabilistic Sensor Network
Routing
Summary
20
A two-threshold scheme
Why?
In a random network, a node may have very
few neighbors, thus the probability that none
of the node’s neighbors will propagate the
gossip is high. We hope that nodes with
lower degree can gossip with higher
probability.
21
GOSSIP2(p1, k, p2, n)


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p1 – typical gossip probability.
k – number of hops with which we gossip
with probability 1.
n – number of neighbors of a node.
p2 – probability for which p2 > p1. Neighbors
of a node with fewer than n neighbors gossip
with probability p2 instead of p1.
22
Comparison of GOSSIP2 with GOSSIP1
GOSSIP2 vs. GOSSIP1 on a random network of average degree 8
GOSSIP2(0.6,4,1,6) has better performance than GOSSIP1(0.75,4), while
using 4% fewer messages than GOSSIP1(0.75,4).
23
Prevent premature gossip
death
The idea behind:
If a node has n neighbors and the gossip
probability is p, for each message, the node
should get roughly pn copies from its
neighbors. If the node gets significantly fewer
than pn copies within a reasonable time
interval, then this is a clue that the message
is dying out.
24
GOSSIP3(p, k, m)
Same as GOSSIP1(p, k) except for the following
modification:
If a node originally did not broadcast a received
message, but then did not get the message from at
least m other nodes within some timeout period,
then the node will broadcast the message
immediately after the timeout period.
Usually m = 1.
25
Comparison of GOSSIP3 with GOSSIP1
GOSSIP3 vs. GOSSIP1 on a random network of average degree 8
GOSSIP3(0.65,4,1) has better performance than GOSSIP1(0.75,4), while
using 8% fewer messages than GOSSIP1(0.75,4).
26
Contents






Introduction
Pure Gossip
Optimization of Gossip
Incorporate Gossip in AODV
Parametric Probabilistic Sensor Network
Routing
Summary
27
Overview of AODV
Using AODV, the first time a node u requests a route to node
v, it uses an expanding-ring search to find the route. That is,
it first tries to find the route in a zone of small radius, by
flooding. It then tries to find the route in zones of larger and
larger radius. If all these attempts fail, it resorts to flooding
the message throughout the whole network. The exact
choice of zone radii to try is a parameter of AODV. Typically,
not too many radii are considered before resorting to flooding
throughout the network.
AODV also maintains a routing table where it stores the route
after it has been found. Every time a packet is sent, the route
in the routing table is tried first.
28
AODV + G (AODV using GOSSIP3)
In AODV, if the expanding-ring search with a
smaller radius fails, rather than flooding to
the whole network, we use GOSSIP3.
In the experiment, GOSSIP3(.65, 1, 1) is
used.
29
Comparison of AODV+G and AODV
Pause time – the time a node pauses after reaching a
randomly set destination. Then the node moves again.
30
Comparison of AODV+G and
AODV (cont.)
Normalized routing load – the number of routing packets
transmitted per data packet delivered at the destination.
31
Comparison of AODV+G and
AODV (cont.)
Route length ratio – the ratio of the actual shortest route
length to the shortest route length found.
32
Contents






Introduction
Pure Gossip
Optimization of Gossip
Incorporate Gossip in AODV
Parametric Probabilistic Sensor Network
Routing
Summary
33
Parametric Probabilistic Sensor
Network Routing
Christopher L. Barrett, Stephan J. Eidenbenz, Lukas Kroc,
Madhav Marathe, James P. Smith (WSNA’03)
DESTINATION ATTRACTOR - the retransmission
probability at a node depends on the distance counted in
hops from the source node to the destination node and
the hop-distance from the node currently holding a
packet to the destination.
DIRECTED TRANSMISSION - the probability depends
on the same two distance factors and additionally on the
number of hops that the packet has already traveled.
34
Notation
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
S – source sensor.
D – destination sensor.
i – number of time steps.
Ri – a sensor holding a packet at time step i.
Ri-1 – the sensor that sent the packet to Ri.
d(Ri, Rj) – hop distance between Ri and Rj.
PRi – retransmission probability of Ri.
At time step i, all sensors who received a packet at the
previous time step i-1 decide whether to retransmit the
packet, and, if affirmative, do so.
35
DESTINATION ATTRACTOR
Idea behind:
If the packet is getting closer to the
destination, then its retransmission
probability is increased; if it is getting
further away from the destination, then
the retransmission probability is
reduced.
36
DESTINATION ATTRACTOR (cont.)
37
DIRECTED TRANSMISSION
Idea behind:
The nodes that lie on a shortest path from
the source to the destination should
forward packets with a very high
probability and the farther away a node is
from the shortest path, the smaller its
retransmission probability should be.
38
DIRECTED TRANSMISSION
(cont.)
Let Ri' denote any node that holds a packet at time i. The
node minimizing minRi'd(Ri', D) is the node closest to the
destination. Thus:
39
Retransmission Probability Contour
40
Experiment


Noise is used to model sensor mobility, node
failure and other inaccuracy.
Protocols tested in the experiment are as
follows:
41
Experiment (cont.)
Experiment Setup:
- 5000 sensors are spread uniformly at
random in a square field, where all sensors
have equal range of transmission, inducing
a graph with average node degree of
approximately 6.7.
- A TDMA model is assumed for the
medium access control (MAC) sublayer.
42
Sample Snapshot of DIRECTED
TRANSMISSION
43
Sample Snapshot of DESTINATION
ATTRACTOR
44
Sample Snapshot of PURE GOSSIP
45
Experiment Result
Load - number of times any sensor transmits a packet.
Lag - number of time steps it takes to deliver the packet to the destination.
Fraction delivered - fraction of runs where the destination receives the data.
The Lag is divided by length of the shortest path from source to destination for
each run to make the runs comparable.
46
Experiment Result (cont.)
47
Experiment Result (cont.)
The parameter of Directed Transmission and Destination
Attractor is k.
The parameter of Gossiping is p.
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Conclusion
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

DESTINATION ATTRACTOR and DIRECTED
TRANSMISSION can guarantee any quality of
service level (measured as fraction delivered) even
in the presence of highly noised network
information.
Multi-path methods outperform single-path methods
in the presence of noise.
Making the retransmission probability depend on
network information parameters is a promising step
towards more robust routing protocols in sensor
networks.
49
Contents






Introduction
Pure Gossip
Optimization of Gossip
Incorporate Gossip in AODV
Parametric Probabilistic Sensor Network
Routing
Summary
50
Summary




Pure Gossip (GOSSIP1).
Optimization of Gossip (GOSSIP2 and
GOSSIP3).
Integrate Gossip with AODV.
Parametric Probabilistic Sensor Network
Routing.
51
References

Zygmunt Haas, Joseph Y. Halpern, Li Li. Gossip-Based Ad Hoc
Routing. Proceedings of INFOCOM 2002, 2002.

Christopher L. Barrett, Stephan J. Eidenbenz, Lukas Kroc, Madhav
Marathe, James P. Smith. Parametric Probabilistic Sensor Network
Routing. WSNA'03.

P.Th.Eugster, R.Guerraoui, S.B.Handurukande, A.M.Kermarrec,
P.Kouznetsov. Lightweight Probabilistic Broadcast. DSN'01.

L. Rodrigues, S. Handurukande, J. Pereira, R. Guerraoui, A.-M.
Kermarrec. Adaptive Gossip-Based Broadcast. DSN'03.

Werner Vogels, Robbert van Renesse, Ken Birman. The Power of
Epidemics: Robust Communication for Large-Scale Distributed
Systems. ACN SIGCOMM, Volume 33, Number 1: January 2003.
52
Thank you!
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