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Self Limiting Epidemic Forwarding and Self Limiting Epidemic Forwarding and Fluid Approximations of Continuous Time Fluid Approximations of Continuous Time

Markov ChainsMarkov Chains

Jean-Yves Le BoudecJean-Yves Le BoudecEPFL/I&C/ISC-LCA-2EPFL/I&C/ISC-LCA-2

jean-yves.leboudec@epfl.chjean-yves.leboudec@epfl.ch ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE

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Contents

1. Self Limiting Epidemic Forwarding2. Control of Spread / TTL3. Performance Evaluation

4. Methodology: deriving fluid model

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Self-Limiting Broadcast

This work is performed in the Haggle EU project: opportunistic networking

We are interested in a broadcast + limited serviceClassical: used in discovery phase of routing protocols

[EASE, SPRAY and FOCUS, HAGGLE FORWARDING]

Also to support apps on their ownChat on a jammed highway, urban areaCoupon application

No assumption about connectivityFrom intermittent to very rich

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Mental Model of Epidemic ForwardingApp

N=2 M= 3 Stored TTL = 221.88 From xxx Text=“…..”

N=6 M= 1 Stored TTL = 221.88 From xxx Text=“…..”

N=4 M= 1 Stored TTL = 221.88 From xxx Text=“…..”

Epidemic Buffer

MAC Layer

N=0 M= 0 Stored TTL = 221.88 From self Text=“…..”

Scheduler

N=5 M= 3 Stored TTL = 221.88 From xxx Text=“…..”

One node

N=2 M= 1 Stored TTL = 221.88 From xxx Text=“…..”

TTL = 34 IP source= …..

Transmitted packet

stored packet

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Performance Issues with Epidemic Forwarding

Known to quickly deteriorate performance “cost of flooding”Many enhancements proposed (e.g. probabilistic forwarding)Enhancements work if magical parameters are set well

We are interested in case where we do have epidemic forwarding and want to make it work for real

E.g. in cars

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Control / performance issues

A Possible classification:1. Control of forwarding factor

How many times a message is repeated The classical issue addressed in the literature

2. Control source injection rates

3. Scheduling

4. Control of spread How many nodes are reached by a message Our focus today

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Spread Control

Limiting the spread is implicitly assumed to be done by TTLBut there are many options and issuesWe present the options then evaluate the performance

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Contents

1. Self Limiting Epidemic Forwarding2. Control of Spread / TTL3. Performance Evaluation

4. Methodology: deriving fluid model

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Classical TTL

Implicitly assumed in almost all existing worksCD: “4 hops is enough”

When receiving a packet for the first time, decrement TTL (if >0) and store in epidemic buffer

When relaying the packet: send with stored TTL If transmit multiple times, all with same stored TTL

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Same as classical TTL but decrement stored TTL for every send event

Equivalent to the forwarding token counter used in “Spray and Focus”

TTL = log2 (token)

Thrasyvoulos Spyropoulos, Konstantinos Psounis, and Cauligi Raghavendra, “Spray and Wait: An Efficient Routing Scheme for Intermittently Connected Mobile Networks,” in proceedings of ACM SIGCOMM workshop on Delay Tolerant Networking (WDTN-05), August 2005

Stored TTL

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Same as TTL but the stored TTL is decremented at receive events

Selective aging:Decrement stored TTL of this packet when a duplicate is receiveGlobal aging:Decrement stored TTL of all packets when any packet is received by some (very) small amount

A fine granularity is obtained by allowing Stored TTL to be non integer

Aging

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Contents

1. Self Limiting Epidemic Forwarding2. Control of Spread / TTL3. Performance Evaluation

4. Methodology: deriving fluid model

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Performance Evaluation

Method: Simulation JIST-SWANS + analytical model with fluid limit ODE of continuous time markov chainPerformance metrics

Spread: number of nodes that receive one messageSpread factor: number of transmission events for one messageInjection rate (for a flow controlled source)Buffer usage

We looked for the applicability of a scheme to a large set of environments

Mobile VANETsInfinite gridInfocom –like traces

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Working Hypotheses

We used a virtual rate scheduler, serves packet no earlier than according to packet’s vrate, otherwise fair queuing per source

Control of forwarding factor done by vrate = a Nrcv Nsnd with a < 1 Self packet is removed when one duplicate is received An issue is support for broadcast

Naive (CTSless) broadcast does not work -> we use Katabi’s Pseudo-Broadcast whenever possible (crowded area), otherwise we revert to CTSless with indication of presenceSee [2] for details

Our implementation of broadcast in Java is now available

[4] and sourceforge

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Findings ClassicalTTL or StoredTTL need to adapt the max TTL to the

environmentRich connectivity (traffic jam) requires a very small max TTL, not suitable in other environments

Worse, in very dense environments, ClassicalTTL and StoredTTL suffer from collapse

In contrast, aging is robust to all situationsThe performance in overall much betterHigher spread and rate with smaller buffer sizes

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agingstoredTTL

Fluid highway

jam

Fluid highway

jam

Fluid highway

jam

Fluid highway

jam

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3

3

3 4

4

4

4

1

1

1

1

2

2

2

2

5

5

5

5

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Results, Infinite Line

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Vulnerabilities

We have also studied vulnerabilities of epidemic forwardingAgainst malicious or rational attacksMalicious:

Artificial High DensityInhibit by ForwardingInhibit by TTLSend on Behalf

RationalDo not cooperateSybil

Findings: malicious attack can work but require static nodes close to victim, does not work well in mobile casesRational attacks always work

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Contents

1. Self Limiting Epidemic Forwarding2. Control of Spread / TTL3. Performance Evaluation

4. Methodology: deriving fluid model

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Markov Model for Epidemic Forwarding

The model is complex, O(AN^2) statesN: nb nodes A: a fixed integer

Can we use simple approximations ? What is the corresponding fluid model ?

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Fluid Model is Often Derived Heuristically[KYBR-2006] R. Kumar, D. Yao, A. Bagchi, K.W. Ross, D. Rubenstein, Fluid

Modeling of Pollution Proliferation in P2P Networks, ACM Sigmetrics 2006, St. Malo, France, 2006

Original (micro-) model is continuous time markov process on finite (but huge) state space

Found too large, replaced by a fluid model Step from micro to fluid is ad-hoc, based on informal reasoning Q1: Is there a formal (mechanical) way to derive the fluid model

from the microscopic description ?

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A Similar Step is Common Place in Chemistry/Biology[L-2006] Jean-Yves Le Boudec, Modelling The Immune SystemToolbox:

Stochastic Reaction Models, infoscience.epfl.ch, doc id: LCA-TEACHING-2007-001

Q2: What is the link between the micro quantities and fluid ones ?

Is the fluid quantity the expectation of a microscopic quantity ? Or a re-scaled approximation ?

Micro modelMarkov process

Fluid model

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The Maths of Physics, Chemistry and Biology Help Us

Infinitesimal generator (drift of f)

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Example of Forward EquationsA Linear Case

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Another, non linear example: SI Model

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See

“Performance Modeling of Epidemic Routing” Ellen(Xiaolan) Zhang, Giovanni Neglia, Jim Kurose, Don Towsley, UMass Computer Science Technical Report 2005-44

for an example where this is used

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A Fluid Limit Theorem

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Towards a Mechanical Derivation of Fluid Model1. Define the state variable2. Pick functions of interest of the state variable3. Define the transitions jumps r and rates hr(x)4. Compute the generator and write the ODE

1. Define the state variable2. Pick functions of interest of the state variable3. Define the transitions jumps r and rates hr(x)4. Compute the generator and write the ODE

What do we obtain from the fluid model ?• transients• stable points

Implemented for models of the type below in the TSED tool at

http://ica1www.epfl.ch/IS/tsed/index.html

Implemented for models of the type below in the TSED tool at

http://ica1www.epfl.ch/IS/tsed/index.html

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Application to Self-Limiting Epidemic Forwarding

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Application to Self-Limiting Epidemic Forwarding

There is description complexity, but no modelling complexity

A: Age of packet sent by node in middle

ODE

simulation

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Other Results That Are Candidate For Automatic Generation of Solution

Hybrid simulationFast transitions simulated as deterministic fluid, slow transitions as stochastic processExample: mobility + message transmission

Mobility modeled as fluidChange in mobility state changes the rate of the process of packet transmission

“Hybrid Simulation Method” based on representation (martingale approach)

Approximation by SDE

Mean Field, Pairwise approximation Other scaling limits derived from generator approach

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References

[1] A. El Fawal, J.-Y. Le Boudec and K. SalamatianPerformance Analysis of Self Limiting Epidemic ForwardingEPFL Technical Report, 2006.

[2] A. El Fawal, J.-Y. Le Boudec and K. SalamatianSelf-Limiting Epidemic ForwardingEPFL Technical Report, 2006.

[3] A. El Fawal, J.-Y. Le Boudec and K. SalamatianVulnerabilities in Epidemic ForwardingEPFL Technical Report, 2006.

[4] MAC layer functions for SLEF / Keller, Lorenzo – 2006 [LCA-STUDENT-2006-005]

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Conclusion

We have investigated a novel approach to TTL management, based on decrement on packet reception

We have shown that it improves the usability of epidemic forwarding to case where it otherwise would congest

It seems possible to use generic simplification approaches borrowed from the modelling of large markov processes