Routing in Intermittently Connected Mobile Networks

1. Routing in Intermittently Connected Mobile Networks Thrasyvoulos Spyropoulos, Kostantinos Psounis, and Cauligi S. Raghavendra EE Department, USC {spyropou, kpsounis, raghu}@usc.edu

2. S D Intermittently Connected Mobile Networks • A wireless network that is very sparse and partitioned • disconnected clusters of nodes • Nodes are (highly) mobile making the clusters change often over time • No contemporaneous end-to-end path! S D

3. Networks following ICMN paradigm • Sensor networks for habitat monitoring and wildlife tracking • ZebraNet: sensor nodes attached on zebras, collecting information about movement patterns, speed, herd size, etc. • Boatnet • Ad hoc networks for low cost Internet provision to remote areas/communities • Africa, Saami, etc. • Inter-planetary networks • extend the idea of Internet to space • Ad-hoc military networks

4. Conventional Routing Protocols Fail • Reactive Protocols (e.g. DSR D. Johnson et al. ‘01, AODV C. Perkins et al. ‘02) • route request cannot reach destination! • path breaks right after or even while being discovered • Proactive Protocols (e.g. DSDV C. Perkins et al. ‘94, DREAM S. Basagni et al. ‘98) • will fail to converge! • deluge of topology-update packets

5. Can anything be done then? A different routing paradigm • Exploit node mobility to deliver messages (Tse et al. exploit mobility to increase capacity) • A snapshot of connectivity graph is always disconnected. Idea: If we overlap many snapshots over time, an end-to-end path will be formed eventually! • Store-and-forward model of routing: • a node stores a message until an appropriate communication opportunity arises • a series of independent forwarding decisions {time + next hop} that will eventually bring the packet to its destination

6. Example of store and forward routing 1 12 D 13 S 14 2 16 11 15 3 7 8 5 10 4 9 6 Main Issue: What is an “appropriate” next hop?

7. Choosing A Next Hop • A local and intuitive criterion: A forwarding step is efficient if it reduces the expected distance from destination • usually: reduction of expected distance => reduction of expected hitting time Destination B A C Efficient Routing : Ensure that each forwarding step on the average reduces distance or hitting time with destination

8. Problem Formulation • M nodes move independently on an grid of size N • mobility models: random walk, random waypoint • Transmission range K • small enough to have partial connectivity • transmission is faster than movement • Proximity measure between positions A and B • Manhattan distance: dAB = |xA – xB| + |yA – yB| • Performance evaluation metrics • expected hitting time from A to B: EATB • in a symmetric graph EATB = ET(dAB) • average delivery delay • number of transmissions (per message delivered)

9. Problem Formulation (cont’d) • Each node maintains a timer for each other node • TX(Y): time since node X last “encountered” node Y • “encounter” = come within transmission range • only information available to a node X regarding the network (no location, speed, direction, etc.) • Timer maintenance • Initially: TX(Y) =  • When X encounters Y: TX(Y) = 0 • At every time step (unless case b applies): TX(Y) = TX(Y) + 1

10. Single-Copy vs. Multiple-Copy Routing Strategies • “Single-Copy”: only a single copy of each message exists in the network at any time • “Multiple-Copy”: multiple copies of a message may exist concurrently in the network Single Copy Multiple Copy + lower number of transmission + lower contention for shared resources + lower delivery delay + higher robustness

11. Outline • Single-copy strategies • design space • Seek and Focus • performance analysis • simulations • Multiple-copy schemes • comparison to single-copy • existing flooding and utility-based schemes • Spray and Wait • performance analysis • simulations

12. Direct Transmission • Forward message only to its destination • simplest strategy • Its expected delay is an upper bound for every other protocol.

13. Randomized Routing • Node A forwards message to node B with probability p • P(B closer to destination D than A) = P(A closer to D than B) • yet, because transmission speed is faster than the speed of movement it can be shown that Result: The randomized policy results in a reduction of the expected hitting time to destination at every step

14. Utility-based Routing • Destination’s location (relative to another node’s location) gets indirectly logged in timer during encounter • Location info gets diffused through mobility process • Define an appropriate utility function UX(Y) based on timer value TX(Y) • e.g. UX(Y) = - expected hitting time given timer value • Utility-based routing: Node A forwards a message for node D to node B iff UA(D) < UB(D) • Now, if TB(D) < TA(D), PBA = P(B closer to D than A) > P(A closer to D than B)

15. Randomized Utility-based PBA = ½ PBA > ½ PAB = ½ PAB < ½ Utility-based Routing (cont’d) ETD EATD = ET(d) d B A B Result 1: Utility-based routing has a larger expected delay reduction than the simple randomized policy

16. Randomized vs. Utility-based Routing • Randomized strategy + transmissions are faster than movement - many transmissions for marginal gain (forwards message blindly) • Utility-based strategy + takes advantages of indirect location info to make better forwarding decisions - slow start: In a large network, source and destination are far => all nodes around source have very low utility => takes a long time until a good next hop is found initially

17. Seek and FocusA Hybrid Routing Strategy • Seek phase: If utility around node is low, perform randomized forwarding to quickly search nearby nodes • Focus phase: When a high utility node (i.e. above a threshold)is discovered, switch to utility-based forwarding • look for a good leadto the destination and follow it IDEA: Avoid the slow start phase of utility-based schemes, while still taking advantage of the higher efficiency of utility-based forwarding

18. Oracle-based Optimal Algorithm • Assume all nodes trajectories (future movements) are known • Then, the algorithm picks the sequence of forwarding decisions that minimizes delay • Note that flooding (multi-copy strategy) has the same delay as this algorithm when there is no contention

19. Performance analysis • Compute expected delivery delay (ED) • Assumptions • mobility model: random walk on grid (torus) • there is no contention in the wireless channel • Notation • EXTY: expected hitting time from X to Y • ET: expected hitting time from stationary distribution (indep. of specific position for symmetric graph)

20. Direct Transmission: K = 0 • ED = ET • Hitting time distribution approximately exponential: • Results from D. Aldous and J. Fill “Reversible Markov chains and random walks on graphs” - - ET = (NlogN)

21. A Direct Transmission: K > 0 1) EDdt = EXTA 2) EXTA = EXTY - EATY EXTY = cNLogN K = 3

22. 2 where HM-1 is the harmonic sum 1 2 Oracle-based Optimal Algorithm M nodes Tx Range = K D S

23. f(K) D Average step size: D = 1 – q + q f(K) Randomized Algorithm Probability q: Tx jump q = p • P(at least one node within range) f(K): average transmission distance Probability 1-q: Random walk

24. Randomized Algorithm (cont’d) • Approximate actual message movement with a random walk performing D independent 1-step moves at each time slot • Note: This walk is slower than the actual walk • would reach destination later, on the average • Define an appropriate martingale to show that: Destination movement Message movement Note: D + 1 ≥ 2  randomized is faster than direct transmission!

25. Simulation vs. Analysis upper bound lower bound Simulation and theoretical results are closely matched Randomized algorithm is efficient for large K

26. Simulated schemes Randomized with probability p = 0.5 Randomized with probability p = 1.0 Utility-based routing Seek and Focus (with probability p = 0.5 in seek phase) Seek and Focus (with probability p = 1.0 in seek phase) Direct transmission Used a simple collision avoidance MAC protocol to handle contention Simulations with contention

27. Scenario 1 (random walk, small network) • 50x50 grid, 20 nodes, transmission range = 5 • Only 1 message is routed between two randomly chosen nodes Randomized (p = 0.5) 4 Seek and Focus (p = 0.5) 1 2 Randomized (p = 1.0) 5 Seek and Focus (p = 1.0) 3 Utility-based 6 Direct

28. Scenario 2 (random walk, large network) • 500x500 grid, 50 nodes, transmission range = 60 • 50 messages are routed between randomly chosen nodes Randomized (p = 0.5) 4 Seek and Focus (p = 0.5) 1 2 Randomized (p = 1.0) 5 Seek and Focus (p = 1.0) 3 Utility-based

29. Scenario 3 (random waypoint) • 500x500 grid, 50 nodes, transmission range = 20 • 50 messages are routed between randomly chosen nodes Randomized (p = 0.5) 4 Seek and Focus (p = 0.5) 1 2 Randomized (p = 1.0) 5 Seek and Focus (p = 1.0) 3 Utility-based

30. Outline • Single-copy strategies • design space • Seek and Focus • performance analysis • simulations • Multiple-copy schemes • comparison to single-copy • existing flooding and utility-based schemes • Spray and Wait • performance analysis • simulations

31. Multiple-copy vs. single-copy Routing + Higher robustness + Low delivery delay - Higher number of transmissions - Contention for shared resources

32. Flooding-based and Utility-based Schemes • Epidemic Routing (flooding): handover a copy to everyone • minimum delay under no contention • Randomized Flooding (Y. Tseng et al. ‘02): handover a copy with probability p • Utility-based Flooding (A. Lindgren et al. ‘03): handover a copy to a node with a utility at least Uth higher than current • Constrained Utility-based Flooding: like previous, but may only forward a bounded number of copies of the same message

33. Shortcomings • Flooding • too many transmissions (energy-efficiency concerns) • unbounded number of copies per message (scalability issues) • under high traffic, high contention for buffer space and bandwidth results in poor performance • Utility-based • high Uth: significant delay increase; source takes a very long time until it finds a good next hop (slow start) • low Uth: degenerates to flooding

34. Spray and Wait • Performance goals: • significantly reduce transmissions by bounding the total number of copies/transmissions per message • under low traffic: minimal penalty on delay (close to optimal) • under high traffic: reduce the delay of existing flooding- and utility-based schemes thanks to less contention • 2 phases: • “Spray phase”: spread L message copies to L distinct relays • “Wait phase”: wait until one of the L relays finds the destination (i.e. use direct transmission)

35. Spray and Wait Variations • Source Spray and Wait • Source starts with L copies • whenever it encounters a new node, it hands one of the L copies • this is the slowest among all (opportunistic) spraying schemes • Optimal Spray and Wait • source starts with L copies • whenever a node with n > 1 copies finds a new node, it hands half of the copies that it carries • optimal spreads the L copies faster than any other spraying scheme

36. Performance analysis • Compute ED, the expected delivery delay • Assumptions • mobility model: random walk on grid • there is no contention in the wireless channel • Recall that EDdt denotes the expected delivery delay of direct transmission

37. If new node found by source, forward another copy If not destination, add extra term Expected remaining delay after i copies are spread Time until a new node is found P(not destination) If found by relay, do nothing Source Spray and Wait • Let ED(i) denote the expected remaining delay after i copies are spread • Clearly EDsrc = ED(1) • ED(1) can be calculated through a system of recursive equations If destination, stop • A similar recursion procedure gives the delay of Optimal Spray and Wait

38. Upper bound • Exact delay not in closed form • Derive a bound in closed form • This is an upper bound for any Spray and Wait algorithm Probability a wait phase is needed Wait Phase Spray Phase Bound is tight for L<<M

39. Simulation vs. Analysis (analysis) • Good match between theory and simulations • Spray and Wait achieves a delay only 1.5-2 times that of the optimal

40. Simulation vs. Analysis (cont’d) (analysis) Efficient spraying becomes more important for large L

41. Simulated schemes Epidemic routing Randomized flooding (p = 0.03) Utility-based flooding (Uth = 0.02) Constrained utility-based flooding Source Spray and Wait (L = 10) Optimal Spray and Wait (L = 10) Seek and Focus Oracle-based optimal algorithm Same collision avoidance MAC protocol and utility function as before Simulations (with contention, waypoint model)

42. Scenario A (low traffic) 500x500, M = 50 nodes, K = 20 • Spray and Wait • performs 60-97% less transmissions (even less than seek and focus) • achieves a lower delay than utility-based schemes that is about twice that of the optimal

43. Scenario B (high traffic) 500x500, M = 50 nodes,K = 20 (6% coverage), 40 (25% coverage) • Spray and Wait achieves up to an order of magnitude reduction in number of transmission compared to flooding and utility-based schemes • and a delivery delay lower than all other schemes

44. Conclusions • Seek and Focus • yields the best tradeoff between delay and number of transmissions among single-copy schemes • Spray and Wait • is as energy efficient as single-copy schemes • yields lower delay than existing flooding- and utility-based schemes, and • this delay is within a factor of 2 from that of optimal

45. Future Work • Analysis of utility-based schemes • Analysis under contention • Explore hybrid schemes where: • L copies are spread initially • Each copy is routed using some efficient single-copy scheme (e.g. utility-based single-copy routing) • Performance of all protocols under more realistic mobility models that exhibit correlation in space and/or time • Capacity Analysis

46. References • A. Spyropoulos, K.Psounis, and C. Raghavendra. Single-copy routing in intermittently connected mobile networks. CENG-2004-11 Technical Report, University of Southern California, June 2004. in IEEE SECON ‘04. • A. Spyropoulos, K.Psounis, and C. Raghavendra. Multi-copy routing in intermittently connected mobile networks. CENG-2004-12 Technical Report, University of Southern California, June 2004.