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

1. Self Limiting Epidemic Forwarding and Fluid Approximations of Continuous Time Markov Chains Jean-Yves Le Boudec EPFL/I&C/ISC-LCA-2 jean-yves.leboudec@epfl.ch 1

2. Contents • Self Limiting Epidemic Forwarding • Control of Spread / TTL • Performance Evaluation • Methodology: deriving fluid model 2

3. Self-Limiting Broadcast • This work is performed in the Haggle EU project: opportunistic networking • We are interested in a broadcast + limited service • Classical: used in discovery phase of routing protocols [EASE, SPRAY and FOCUS, HAGGLE FORWARDING] • Also to support apps on their own • Chat on a jammed highway, urban area • Coupon application • No assumption about connectivity • From intermittent to very rich 3

4. Mental Model of Epidemic Forwarding N=0 M= 0 Stored TTL = 221.88 From self Text=“…..” N=2 M= 1 Stored TTL = 221.88 From xxx Text=“…..” TTL = 34 IP source= ….. N=5 M= 3 Stored TTL = 221.88 From xxx Text=“…..” App One node Epidemic Buffer N=2 M= 3 Stored TTL = 221.88 From xxx Text=“…..” N=6 M= 1 Stored TTL = 221.88 From xxx Text=“…..” Transmitted packet N=4 M= 1 Stored TTL = 221.88 From xxx Text=“…..” stored packet Scheduler MAC Layer 4

5. 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 5

6. Control / performance issues • A Possible classification: • Control of forwarding factor • How many times a message is repeated • The classical issue addressed in the literature • Control source injection rates • Scheduling • Control of spread • How many nodes are reached by a message • Our focus today 6

7. Spread Control • Limiting the spread is implicitly assumed to be done by TTL • But there are many options and issues • We present the options then evaluate the performance 7

8. Contents • Self Limiting Epidemic Forwarding • Control of Spread / TTL • Performance Evaluation • Methodology: deriving fluid model 8

9. Classical TTL • Implicitly assumed in almost all existing works • CD: “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 9

10. Stored TTL • 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 10

11. Aging • Same as TTL but the stored TTL is decremented at receive events • Selective aging:Decrement stored TTL of this packet when a duplicate is receive • Global 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 11

12. Contents • Self Limiting Epidemic Forwarding • Control of Spread / TTL • Performance Evaluation • Methodology: deriving fluid model 12

13. Performance Evaluation • Method: • Simulation JIST-SWANS + analytical model with fluid limit ODE of continuous time markov chain • Performance metrics • Spread: number of nodes that receive one message • Spread factor: number of transmission events for one message • Injection rate (for a flow controlled source) • Buffer usage • We looked for the applicability of a scheme to a large set of environments • Mobile VANETs • Infinite grid • Infocom –like traces 13

14. 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 14

15. Findings • ClassicalTTL or StoredTTL need to adapt the max TTL to the environment • Rich 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 situations • The performance in overall much better • Higher spread and rate with smaller buffer sizes 15

16. 1 2 5 3 4 3 2 1 5 4 1 3 2 1 5 4 3 4 5 2 storedTTL aging jam Fluid highway Fluid highway jam Fluid highway Fluid highway jam jam 16

17. Results, Infinite Line 17

18. Vulnerabilities • We have also studied vulnerabilities of epidemic forwarding • Against malicious or rational attacks • Malicious: • Artificial High Density • Inhibit by Forwarding • Inhibit by TTL • Send on Behalf • Rational • Do not cooperate • Sybil • Findings: • malicious attack can work but require static nodes close to victim, does not work well in mobile cases • Rational attacks always work 18

19. Contents • Self Limiting Epidemic Forwarding • Control of Spread / TTL • Performance Evaluation • Methodology: deriving fluid model 19

20. 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 ? 20

21. 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 ? 21

22. A Similar Step is Common Place in Chemistry/Biology Fluid model Micro model Markov process [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 ? 22

23. The Maths of Physics, Chemistry and Biology Help Us Infinitesimal generator (drift of f) 23

24. Example of Forward EquationsA Linear Case 24

25. Another, non linear example: SI Model 25

26. 26

27. See “Performance Modeling of Epidemic Routing” Ellen(Xiaolan) Zhang, Giovanni Neglia, Jim Kurose, Don Towsley, UMass Computer Science Technical Report 2005-44for an example where this is used 27

28. A Fluid Limit Theorem 28

29. Towards a Mechanical Derivation of Fluid Model • Define the state variable • Pick functions of interest of the state variable • Define the transitions jumps r and rates hr(x) • Compute the generator and write the ODE • Implemented for models of the type below in the TSED tool at http://ica1www.epfl.ch/IS/tsed/index.html • What do we obtain from the fluid model ? • transients • stable points 29

30. Application to Self-Limiting Epidemic Forwarding 30

31. There is description complexity, but no modelling complexity Application to Self-Limiting Epidemic Forwarding A: Age of packet sent by node in middle ODE simulation 31

32. Other Results That Are Candidate For Automatic Generation of Solution • Hybrid simulation • Fast transitions simulated as deterministic fluid, slow transitions as stochastic process • Example: mobility + message transmission • Mobility modeled as fluid • Change 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 32

33. 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] 33

34. 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 34