Fast, Faster, and Correct

Roy FriedmanTechnionHaifaIsrael

Based on work and discussions with Vadim Drabkin and Gabi Kliot

Talk Overview

Some recent experience with probabilistic flooding/gossip in ad-hoc networks Theoretical analysis, resulting in some design

guidelines A protocol that follows those guidelines and its

performance analysis

Implications to P2P Some rules of thumbs for developing efficient

gossip protocols

Ad-Hoc Networks

Devices equipped with omni-directional wireless antennas Can transmit messages to all other nodes within a

given transmission range R Transmission disk model

By forwarding messages, a multiple-hop network is formed

p qp q

Transmission Overlap

On average, the transmission range of two neighboring nodes is 39% [Tseng et al. 2002]

So, how many nodes should rebroadcast a message to ensure broadcast delivery with high probability?

Reliability vs. # Transmissions

Probability that an arbitrary node does not receive a message

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

1 2 3 4 5 6 7 8 9 10

Beta

Non

rec

eive

pro

babi

lity

Successfull transmission probability 1

Successfull transmission probability 0.8

Successfull transmission probability 0.6

Our Conclusions for MANETs

The number of senders in each one-hop neighborhood should be a small constant (w.r.t. the network density)

Given the concaved shape of the graph It is best to use probabilistic forwarding up to some

point Then boost the reliability using deterministic

corrective measures

RAPID

A protocol that follows these design rules The probability of forwarding a message is min(1,β/Nr), where Nr is the number of locally observed neighbors, and β the number from the optimal graph (2.5)

We use staggering to reduce collisions If during the staggering one of the neighbors of p retransmits

the message, then the retransmission of p is aborted If no neighbor retransmits the message after a longer timeout,

then p retransmit it We use periodic deterministic gossiping of message headers

A node that discovers that it is missing a message m, asks for m from the gossiper

There is also a version that tolerates selfish and malicious behavior

Purely

randomR

andom/

deterministic

Determ

inistic

Rapid Performance: Reliability

Rapid Performance: Overhead

Rapid Performance

Rapid Performance

What About P2P?

Analyzing random gossip using bins and balls (Boris Koldehofe 2002) n nodes/binsm random forwarding of a message/balls The reliability is then

nmne /

The Reliability of Gossip

# retransmissions

# of

non

-rec

eive

rs

High Availability 101

Suppose the probability of a simple PC is 0.99 The probability that two PCs will be down at

the same time is 1-[(1-0.99)^2]=0.9999 Since a PC is much cheaper than an FT

computer, one should use clusters for HA

Can we Apply the HA Principles for Gossip?

That is, can we use two concurrent cheap/fast probabilistic gossip processes instead of a single heavyweight one?

Answer: It depends on our cost model and how truly random

the probabilistic process is For example, if the probabilistic process is perfect, and the

cost is the number of messages, then the only way to boost the performance is using determinism

If the cost vs. reliability function is heavy tailed, then we can also gain from multiple random processes

Possible Good Cases

Fast probabilistic dissemination, combined with periodic gossip of headers (push+pull) Since headers are shorter than messages, we can

win here probabilistically

Whenever the probabilistic process is not purely random E.g., suppose the dissemination is made to partial

views obtained with an lpbcast like membership mechanism

Here two independent processes have a chance to correct the imperfectness of each other

Conclusions

Probabilistic gossip/flooding is a simple, robust, and effective mechanism to disseminate a message to a large percentage of the nodes

Beyond that, in some cases we can boost the reliability by having two concurrent probabilistic processes, but in many cases it does not make sense

To obtain very high reliability, it is best to complement the probabilistic process with a deterministic recovery one

Open Issues

Identifying when it is possible to boost the performance with two independent processes

Incorporating biased gossip

What kind of deterministic corrective measures can be applied in P2P environments?