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
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
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
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
Outline • Network model • Related work • Ordinary Differential Equation Model • Summary and future work University of Massachusetts, Amherst
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
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
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
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
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
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
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
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
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
Extensions • Extensible to other schemes Epidemic routing 2-hop forwarding Prob. forwarding Matching results from Markov chain model, obtained much easier
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
Average delay under varying N Average delay under epidemic routing ODE provides good prediction on average delay
Delay distribution CDF of delay under epidemic routing, N=160 Modeling error mainly due to approx. of ODE
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
Future works • Model storage/transmission overhead of anti-pkts • Evaluate schemes such as spray and wait University of Massachusetts, Amherst
Questions ? Comments ? Thanks! University of Massachusetts, Amherst
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
