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

2. 2 Contents 1.Self Limiting Epidemic Forwarding 2.Control of Spread / TTL 3.Performance Evaluation 4.Methodology: deriving fluid model

3. 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

4. 4 Mental Model of Epidemic Forwarding App 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

5. 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

6. 6 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

7. 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

8. 8 Contents 1.Self Limiting Epidemic Forwarding 2.Control of Spread / TTL 3.Performance Evaluation 4.Methodology: deriving fluid model

9. 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

10. 10  Same as classical TTL but decrement stored TTL for every send event  Equivalent to the forwarding token counter used in “Spray and Focus” TTL = log 2 (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 2005Spray and Wait: An Efficient Routing Scheme for Intermittently Connected Mobile Networks Stored TTL

11. 11  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 Aging

12. 12 Contents 1.Self Limiting Epidemic Forwarding 2.Control of Spread / TTL 3.Performance Evaluation 4.Methodology: deriving fluid model

13. 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

14. 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 presence See [2] for details Our implementation of broadcast in Java is now available [4] and sourceforge

15. 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

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

17. 17 Results, Infinite Line

18. 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

19. 19 Contents 1.Self Limiting Epidemic Forwarding 2.Control of Spread / TTL 3.Performance Evaluation 4.Methodology: deriving fluid model

20. 20 Markov Model for Epidemic Forwarding  The model is complex, O(A N^2 ) states N: nb nodes A: a fixed integer  Can we use simple approximations ? What is the corresponding fluid model ?

21. 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 ?

22. 22 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 model Markov process Fluid model

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

24. 24 Example of Forward Equations A Linear Case

25. 25 Another, non linear example: SI Model

26. 26

27. 27  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

28. 28 A Fluid Limit Theorem

29. 29 Towards a Mechanical Derivation of Fluid Model 1.Define the state variable 2.Pick functions of interest of the state variable 3.Define the transitions jumps  r and rates h r (x) 4.Compute the generator and write the ODE 1.Define the state variable 2.Pick functions of interest of the state variable 3.Define the transitions jumps  r and rates h r (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 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 http://ica1www.epfl.ch/IS/tsed/index.html

30. 30 Application to Self-Limiting Epidemic Forwarding

31. 31 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

32. 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

33. 33 References [1] A. El Fawal[1] A. El Fawal, J.-Y. Le Boudec and K. Salamatian Performance Analysis of Self Limiting Epidemic Forwarding EPFL Technical Report, 2006. J.-Y. Le BoudecK. Salamatian [2] A. El Fawal[2] A. El Fawal, J.-Y. Le Boudec and K. Salamatian Self-Limiting Epidemic Forwarding EPFL Technical Report, 2006. J.-Y. Le BoudecK. Salamatian [3] A. El Fawal[3] A. El Fawal, J.-Y. Le Boudec and K. Salamatian Vulnerabilities in Epidemic Forwarding EPFL Technical Report, 2006.J.-Y. Le BoudecK. Salamatian [4] MAC layer functions for SLEF / Keller, Lorenzo – 2006 [LCA- STUDENT-2006-005] Keller, Lorenzo

34. 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