Performance Modeling of Epidemic Routing

1. Performance Modeling of Epidemic Routing Xiaolan Zhang, Giovanni Neglia§, Jim Kurose, Don Towsley Department of Computer Science University of Massachusetts at Amherst §Università degli Studi di Palermo

2. Disruption/Delay Tolerant Network (DTN) • Network with intermittent connectivity • Limited/no infrastructure => ad hoc network • Mobility and sparse settings => frequent partition • Examples: • Vehicular network: DakNet, UMassDieselNet • Sparse mobile sensor networks: ZebraNet, under water sensor networks • Disaster relief team/military ad hoc network • Resource constrained: power, bandwidth, storage University of Massachusetts, Amherst

3. Routing in DTN • Adopt store-carry-forward paradigm • “Stateless” routing: forwarding decisions not dependent on node identity, mobility patterns, time of the day etc. • Epidemic routing, K-hop/probabilistic/ limited-time forwarding • Intelligent routing • Probabilistic routing[lindgren03], MaxProp [burgess06] etc. University of Massachusetts, Amherst

4. Epidemic style routing • Epidemic routing: packet propagation => disease spreading [vahdat00] • Whenever “infected” node meets “susceptible” node, a copy is forwarded • Achieve min. delay at cost of trans. power, storage • Trade-off delay for resource (power, storage) • K-hop/probabilistic/limited-time forwarding • Contribution: rigorous, unified ODE-based framework to study performance of DTN routing schemes University of Massachusetts, Amherst

5. Outline • Network model • Related work • Ordinary Differential Equation Model • Summary and future work University of Massachusetts, Amherst

6. 2 2 S D S D D 1 1 1 1 Network setting • N+1 nodes • Random waypoint/direction model • fixed, small transmission range, r • Infinite bandwidth, unlimited buffer

7. Forwarding & recovery schemes • Forwarding schemes • Epidemic routing • K-hop/probabilistic/limited-time forwarding • Recovery: deletion of obsolete copies after delivery to dest., e.g., • IMMUNE: dest. cures infected nodes • VACCINE: on pkt delivery, dest propagates anti-pkt through network University of Massachusetts, Amherst

8. Performance metrics • Under infinite bandwidth, unlimited buffer, different pkts propagate independently • For a pkt in the network • Delivery delay, the time from pkt generated at source until delivery to dest, Td • Avg. num. of copies in system by delivery time, C • Avg. total num. of copies made, G • Avg. buffer occupancy University of Massachusetts, Amherst

9. Related work: hybrid analytic/simulation model • ODE model [small03] • Delivery delay under basic epidemic routing • Involve avg. pair-wise meeting rate obtained from simulation • Markov chain model [haas06] • N-1 parameters to capture nodes mobility (obtained from simulations) • Numerical solution complexity increases with N University of Massachusetts, Amherst

10. Related work: model random contacts [Groenevelt05] • Pair-wise inter-meeting time is close to exponentialrandom variables, if • Nodes move according to random waypoint or random direction mobility • Trans. range r small compared to network area A, • Velocity sufficiently high λ: pair-wise meeting rate w: mobility specific constantr: transmission range V*: average relative speed A: terrain area University of Massachusetts, Amherst

11. 1 2 3 N-2 N N-1 A Related work: a Markov model [groenevelt05] • N+1 nodes, pair-wise meeting rate: • States: NI=1,…, N: num. of infected node, not delivered; A: delivered • Transient analysis to derive delay, copies made by delivery; hard to obtain closed form, even so for more complex schemes Infection rate: Delivery rate: University of Massachusetts, Amherst

12. ODE as fluid limit of Markov model • Rewrite transition rate rN(NI)=λNI(N-NI)=N(λN)(NI/N)(1-NI/N) density-dependent form (if remains constant) • [Kurtz70] as N→∞, NI/N → i(t), , initial condition (i.e., initially a given fraction of nodes are infected) • For sufficiently large N and initially infected node, NI(t) is close to I(t): University of Massachusetts, Amherst

13. Derive delivery delay • Delivery delay Td: time from pkt generation at the src until the dest. receives the pkt • CDF of Td, P(t) := Pr(Td<t) given by: • Average delay • Avg. num. of copies sent by delivery prob. that pkt is not delivered yet delivery rate at time t rate that infected nodes meet dest node. University of Massachusetts, Amherst

14. Derive copies sent & storage • Consider recovery process, eg IMMUNE (dest. node cures infected nodes): • Total num. of copies made: • Total buffer usage R(t): num. of recovered nodes Num. of susceptible nodes University of Massachusetts, Amherst

15. Extensions • Extensible to other schemes Epidemic routing 2-hop forwarding Prob. forwarding Matching results from Markov chain model, obtained much easier

16. Model validation through simulation • Our own simulator: • Ignore physical/MAC layer details • Setting • Square area: 20 x 20 with wrap-around boundary • Transmission range r=0.1 • Random direction model • Speed chosen uniformly in [4,10] • Trip duration: exp. with mean 0.25 • Resulting pair-wise meeting rate University of Massachusetts, Amherst

17. Average delay under varying N Average delay under epidemic routing ODE provides good prediction on average delay

18. Delay distribution CDF of delay under epidemic routing, N=160 Modeling error mainly due to approx. of ODE

19. Summary • ODE model for epidemic style routing • As limiting process of Markov Chain • Study metrics: delay, copies made, storage • Easier to derive closed form results; numerical solution complexity does not increase with N • Extensions to various schemes • Model validation through simulation • Not covered here: ODE with second moment, buffer constrained case University of Massachusetts, Amherst

20. Future works • Model storage/transmission overhead of anti-pkts • Evaluate schemes such as spray and wait University of Massachusetts, Amherst

21. Questions ? Comments ? Thanks! University of Massachusetts, Amherst

22. Poisson Meeting Process • Example settings considered in [groenevelt05] • Terrain: 4 km X 4 km • Transmission range: r=50/100/250 m • Speed in [4,10] km/h • Trip duration (for random direction): exp. with mean ¼ hr University of Massachusetts, Amherst