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CS 525 Advanced Distributed Systems

Spring 09

Indranil GuptaLecture 7

More on Epidemics (or “Tipping Point Protocols”)February 12, 2009

(gatorlog.com)(epath.org)

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Question…What fraction of main roads need to be randomly knocked out before source and destination are completely cut off?

Destination

Source

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Critical Value? Answer = 0.5

Tipping Point!

Source

Destination

(Comes from Percolation Theory)

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“Tipping Point”

[Malcolm Gladwell, The Tipping Point, Little Brown and Company, ISBN: 0316346624]

Tipping is that (magic) moment when an idea, trend or social behavior crosses a threshold, and spreads like wildfire.

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Epidemic Protocols

• A specific class of tipping point protocols• Local behavior at each node – probabilistic• Determines global, emergent behavior at the scale of the

distributed system• As one tunes up the local probabilities, the global

behavior may undergo a threshold behavior (or, a phase change)

• Three papers:1. Epidemic algorithms2. Bimodal multicast3. PBBF (sensor networks)

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Epidemic Algorithms for Replicated Database Maintenance

Alan Demers et. al.

Xerox Palo Alto Research Center

PODC 1987

[Some slides borrowed from presentation by: R. Ganti and P. Jayachandran]

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Introduction

• Maintain mutual consistency of updates in a distributed and replicated database

• Used in Clearinghouse database – developed in Xerox PARC and used for many years

• First cut approaches – Direct mail: send updates to all nodes

• Timely and efficient, but unreliable

– Anti-entropy: exchange database content with random site • Reliable, but slower than direct mail and uses more resources

– Rumor mongering: exchange only ‘hot rumor’ updates• Less reliable than anti-entropy, but uses fewer resources

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Epidemic Multicast

Protocol Protocol roundsrounds (local clock) (local clock)

b b random targets per roundrandom targets per round

UninfectedUninfected

InfectedInfected

Gossip Message (UDP)Gossip Message (UDP)

(from Lecture 1)

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Epidemic Multicast (Push)

Protocol Protocol roundsrounds (local clock) (local clock)

b b random targets per roundrandom targets per round

UninfectedUninfected

InfectedInfected

Gossip Message (UDP)Gossip Message (UDP)

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Epidemic Multicast (Pull)

Protocol Protocol roundsrounds (local clock) (local clock)

b b random targets per roundrandom targets per round

UninfectedUninfected

InfectedInfected

Gossip Message (UDP)Gossip Message (UDP)

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Pull > Push

• Pull converges faster than push, thus providing better delay

• Push-pull hybrid variant possible (see Karp and Shenker’s “Randomized Rumor Spreading”)

p i 1 p i2

p i 1 p i 11n

n 1 p i

Pull

Push

pi – Probability that a node is susceptible after the ith round

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Anti-entropy: Optimizations

• Maintain checksum, compare databases if checksums unequal

• Maintain recent update lists for time T, exchange lists first

• Maintain inverted index of database by timestamp; exchange information in reverse timestamp order, incrementally re-compute checksums

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Epidemic Flavors

• Blind vs. Feedback– Blind: lose interest to gossip with probability 1/k every

time you gossip

– Feedback: Loss of interest with probability 1/k only when recipient already knows the rumor

• Counter vs. Coin– Coin: above variants

– Counter: Lose interest completely after k unnecessary contacts. Can be combined with blind.

• Push vs. Pull

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Deletion and Death Certificates• Absence of item does not spread; On the contrary, it

can get resurrected!• Use of death certificates (DCs) – when a node

receives a DC, old copy of data is deleted• How long to maintain a DC?

– Typically twice (or some multiple of) the time to spread the information

– Alternately, use Chandy and Lamport snapshot algorithm to ensure all nodes have received

– Certain sites maintain dormant DCs for a longer duration; re-awakened if item seen again

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Performance Metrics

• Residue: Fraction of susceptibles left when epidemic finishes

• Traffic: (Total update traffic) / (No. of sites)

• Delay: Average time for receiving update and maximum time for receiving update

• Some results:– Counters and feedback improve delay– Pull provides lower delay than push

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Performance Evaluation

Tipping Point Behavior

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Discussion

Pick your favorite:• Push vs. pull vs. push-pull

– Name one disadvantage of each

• Direct mail vs. anti-entropy vs. rumor mongering– Name one disadvantage of each

• Random neigbhor picking– Disadvantage in wired networks?

– In Sensor network?

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Bimodal Multicast

Kenneth P. Birman et. al.

ACM TOCS 1999

[Some slides borrowed from presentation by: W. Fagen and L. Cook]

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“Traditional” Multicast Protocols

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Vs. Pbcast

• Atomicity: All or none delivery

• Multicast stability: Reliable immediately delivery of messages

• Scalability: Bad. Costs >= quadratic with group size.

• Ordering

• Atomicity: Bimodal delivery guarantee, almost all or almost none (immediately)

• Multicast stability: Reliable eventual delivery of messages

• Scalability: Costs logarithmic w.r.t. network size. Throughput stability.

• Ordering

Traditional Multicast Pbcast

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Pbcast: Probabilistic Broadcast Protocol

• Pbcast has two stages:1. Unreliable, hierarchical, best-effort broadcast.

Eg. IP Multicast

2. Two-phase anti-entropy protocol: runs simultaneously with the broadcast messages

• First phase detects message loss

• Second phase corrects such losses

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The second stage

• Anti-entropy round:– Gossip Messages:

• Each process chooses another random process and sends a summary of its recent messages

– Solicitation Messages:• Messages sent back to the sender of the gossip message requesting a

resend of a given set of messages (not necessarily the original source)– Message Resend:

• Upon reception of a solicitation message, the sender resends that message

• Protocol parameters at each node– # of rounds and # of processes contacted in each round– Product of above two parameters called fanout

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Optimizations

• Soft-Failure Detection: Retransmission requests served only if received recently; protects against congestion caused due to redundant retransmissions

• Round Retransmission Limit: Limit the no. of retransmissions in a round; spread overhead in space and time

• Most-Recent-First Retransmission: prefer recent messages

• Independent Numbering of Rounds: Allows delivery and garbage collection to be entirely a local decision

• Multicast for Some Retransmissions

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Bimodality of Pbcast

Almost none Almost all

LogarithmicY-axis

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Latency for Delivery

Logarithmic growth

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Throughput Comparison

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Discussion

• Disadvantages of Bimodal Multicast?– When would wasteful messages be sent?

• What happens when– Rate of injection of multicasts is very very low?– IP multicast is very very reliable?– IP multicast is very very unreliable?

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PBBF: Probability-Based Broadcast Forwarding

Cigdem Sengul and Matt Miller

ICDCS 2005 and ACM TOSN 2008

(Originated from a 525 Project)

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Broadcast in an Ad-Hoc Network• Ad-hoc sensor network (Grid example below)• One node has a piece of information that it needs to broadcast: e.g., (1)

code update, (2) query• Simple approach: each node floods received message to all its neighbors

– Disadvantages?

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IEEE 802.11 PSM

A real, stable MAC protocol (similar results for S-MAC, T-MAC, etc.)

• Nodes are assumed to be synchronized• Every beacon interval (BI), all nodes wake up for

an ATIM window (AW)• During the AW, nodes advertise any traffic that

they have queued• After the AW, nodes remain active if they expect

to send or receive data based on advertisements; otherwise nodes return to sleep until the next BI

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Protocol Extreme #1

A

N1

N2

N3

D

A = ATIM Pkt

D = Data Pkt

N2N1 N3

A

D

A

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Protocol Extreme #2

N1

N2

N3

D

A = ATIM Pkt

D = Data Pkt

D

D

A

N2N1 N3

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Probability-Based Broadcast Forwarding (PBBF)

• Introduce two parameters to sleep scheduling protocols: p and q

• When a node is scheduled to sleep, it will remain active with probability q

• When a node receives a broadcast, it rebroadcasts immediately with probability p– With probability (1-p), the node will wait and

advertise the packet during the next AW before rebroadcasting the packet

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Analysis: Reliability• Phase transition

when:

pq + (1-p) ≈ 0.8-0.85• Larger than

traditional bond percolation threshold– Boundary effects

– Different metric

• Still shows phase transition

qp=

0.25

p=0.

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p=0.

5

p=0.

75

Fra

ctio

n of

Bro

adca

sts

Rec

eive

d by

99%

of

Nod

es

Tipping Point!

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Application: Energy and LatencyEnergy

Joules/Broadcast

q

LatencyAverage 5-Hop Latency

PBBF

Increasing p

q≈ 1 + q * [(BI - AW)/AW]

Ns2 simulation: 50 nodes, uniform placement, 10 avg. neighbors

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Adaptive PBBFE

nerg

y

Latency

Achievable Region

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Adaptive PBBF (TOSN paper)• Dynamically adjusting p

and q to converge to user-specified QoS metrics– Code updates prefer

reliability overl latency– Queries prefer latency

over reliability

• Can specify any 2 of energy, latency, and reliability

• Subject to those constraints, p and q are adjusted to achieve the highest reliability possible Time

0.0

1.0

0.5q

p

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Discussion

• PBBF: bond percolation (remove roads from city)• Haas et al paper (Infocom): site percolation

– Remove intersections/junctions (not roads) from city

• Site percolation and bond percolation have different thresholds and behaviors

• Hybrid possible? (like push-pull?)• What about over-hearing optimizations? (like

feedback)

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Question…Are there other tipping point protocols…?

Destination

Source

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Next Week Onwards

• Student Presentations start (see instructions)

• Reviews needed (see instructions)

• Project Meetings start (see newsgroup)– Think about which testbed you need access to:

PlanetLab, Emulab, Cirrus

• Tomorrow: Yahoo! Training seminar