Wireless networks routing: Approaches

1. reactive & proactive approaches being standardized optimization approach provably optimal properties routing in delay/disruption tolerant networks a different paradigm other approaches cross-layer design, network coding, … Wireless networks routing: Approaches

2. S D Delay/disruption tolerant networks • Intermittent connectivity • Nodes mobile S D

3. Conventional routing protocols fail • Reactive protocols (e.g. DSR, AODV) • route request cannot reach destination! • path breaks right after or even while being discovered • Proactive protocols (e.g. DSDV) • will fail to converge! • deluge of topology-update packets

4. A different routing paradigm • Exploit node mobility to deliver messages 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

5. 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?

6. 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

7. Single copy strategy • Direct transmission • Source only forwards message to destination • Randomized routing • Node A forwards message to node B with probability p • Other schemes? • Design tradeoff? • Delay versus resource (power, storage)

8. Multicopy strategy • Epidemic routing • Spread of “disease” • Whenever “infected” node meets “susceptible” node, a copy is forwarded • Probabilistic forwarding • When “infected” node meets “susceptible” node, a copy is forwarded w/ prob. of p • Other schemes? • Design tradeoff? • Delay versus resource (power, storage)

9. DTN routing schemes • Design space large • Single-copy or multi-copy? • Single-copy • Which node to forward to? When? • Multi-copy • Which nodes to forward to? When? • Who is allowed to forward? • How to limit the # of copies in network? • Once delivered to destination, how to “recover”? • How to evaluate schemes? • Simulation? Analysis (what techniques)?

10. Problem formulation & schemes • Problem formulation • Single-copy strategy • Schemes • performance analysis • simulations • Multi-copy strategy • Schemes • performance analysis • simulations

11. 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 • Use beaconing to know its neighbors • Proximity measure between positions A and B • Manhattan distance: dAB = |xA – xB| + |yA – yB| • Performance evaluation metrics • average delivery delay • number of transmissions (per message delivered)

12. Problem Formulation (cont’d) • Each node maintains a timer for each other node • TX(Y): time elapsed since X last “encountered” 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

13. Single-copy schemes • Direct transmission • Randomized routing • Utility-based routing • Seek and focus • Oracle-based optimal algorithm

14. Direct transmission • Only forward to destination + Single transmission - Slow: baseline scheme expected delay is an upper bound for any other protocol

15. Randomized routing • A forwards message to B with probability p • B is not allowed to forward it back to A for a given amount of time • Property • Blind forwarding • yet, because transmission is faster than movement, forwarding a message results in a reduction of the expected delivery time to destination

16. Utility-based Routing • In most mobility models, if TB(D) < TA(D), P(B closer to D than A) > P(A closer to D than B) • Define an appropriate utility function UX(Y) based on timer value TX(Y) • UX(Y) is a monotonically decreasing function of TX(Y) • Utility-based routing: Node A forwards a message for node D to node B iff UA(D) < UB(D)

17. 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

18. Seek and focus IDEA: Avoid the slow start phase of utility-based schemes, while still taking advantage of the higher efficiency of utility-based forwarding • 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

19. Oracle-based optimal algorithm • Assume all nodes trajectories (future movements) are known • Then, picks the sequence of forwarding decisions that minimizes delay • Note that epidemic routing has the same delay as this algorithm when there is no contention

20. Performance analysis • Metric: expected delivery delay (ED) • Assumptions • mobility model: random walk on grid (torus) • no contention in the wireless channel • no limit in buffer space • Hitting time • time takes to “encounter” destination (within transmission range) • EXTY: expected hitting time from X to Y • ET: expected hitting time from stationary distribution

21. 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)

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

23. 2 where HM-1 is the harmonic sum 1 2 Oracle-based optimal algorithm • M nodes • Tx Range = K D S

24. 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

25. 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!

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

27. 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 MAC: slotted CSMA to handle contention Simulations with contention

28. Seek and Focus (p = 0.5) 4 Utility-based 3 5 Seek and Focus (p = 1.0) Scenario 1 (random walk) • 500x500 grid, 50 nodes, transmission range = 60 • 50 messages are routed between randomly chosen nodes Randomized (p = 0.5) 1 2 Randomized (p = 1.0) • Randomized routing: low delay, many trans. • utility based: slow, # of transmission small. • Seek and focus: low delay, # of transmission small

29. Multi-copy schemes • Epidemic Routing (flooding): handover a copy to everyone • minimum delay under no contention • Randomized Flooding: handover a copy w/ probability p • Utility-based Flooding: handover a copy to a node w/ 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

30. Spray and wait • Performance goals • significantly reduce transmissions by bounding the total # 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)

31. 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 • spreads the L copies faster than any other spraying scheme

32. Performance analysis • Metric: expected delivery delay (ED) • Assumptions • mobility model: random walk on grid (torus) • no contention in the wireless channel • no limit in buffer space • Recall EDdt denotes the expected delivery delay of direct transmission

33. 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 • ED(i): 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

34. 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

35. How to choose L? • Determine a delay to be achieved • Solve for L • Use recursive equation • Use upper bound

36. 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

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

38. 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)

39. Scenario A (low traffic) 500x500, M = 50 nodes, K = 20 • Spray and Wait • Low delay (twice that of the optimal), small # of transmissions (even less than seek and focus) • achieves a lower delay than utility-based schemes

40. Scenario B (high traffic) 500x500, M = 50, 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

41. Performance of multi-copy routing: other approaches • Use Markov chains • Use ordinary difference equations (limits of Markovian models for large # of nodes) • Flexible • Much easier than using Markov chains • Also models • recovery from “epidemic” • resource usage (buffer usage, # of copies sent) • See reading list

42. Summary • Routing in DTNs • Store & forward: a new paradigm • Single-copy schemes • Multi-copy schemes • Analysis & simulation of several schemes

43. Other routing approaches • Cross-layer design • Combined w/ network coding • …