Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective

1. Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective Gaurav Sharma,Ravi Mazumdar,Ness Shroff IEEE/ACM Transaction on Networking, Vol 15,No 5. 2007, pp981-991 d96725002 蕭 鉢d96725011 黃文莉 r96725035 林意婷 指導老師: 林永松 教授

2. Is node mobility a “liability” or an “asset” in ad hoc networks?

3. Liability • Hand-off protocols for cellular networks [Toh & Akyol] • Adverse effect on the performance of traditional ad hoc routing protocols [Bai, Sadagopan and Helmy] • Asset • Grossglauser and Tse showed node mobility can increase the capacity of an ad hoc network, if properly exploited. • The delay related issues were not considered.

4. To Provide better understanding of the delay and capacity trade-offs in mobile ad hoc networks (MANET) from a global perspective

5. Outlines • Introduction • Capacity scaling of ad hoc networks • Mobility can increase capacity • Main contributions • Main Results • Overview • The Models • Hybrid random walk model • i.i.d mobility model • Random walk model • Hybrid random direction model • Discrete random direction model • Brownian motion mobility • Critical Delay and 2-hops Delay • Critical Delay and 2-hops Delay Under Various Mobility Models • Lower bound on critical delay for hybrid random walk models • Upper bound on critical delay for hybrid random walk models • Lower bound on critical delay for discrete random direction models • Upper bound on critical delay for discrete random direction models • Discussion • Characteristic path length • Conclusion

6. Introduction

7. Capacity scaling of ad hoc networks • Study fundamental properties of large wireless networks [Gupta & Kumar] • Derive asymptotic bounds for throughput capacity • To derive upper bounds, use: • Interference penalty—nodes within range need to be silenced for successful communication • Multi-hop relaying penalty— a node that traverses a distance of d needs to use order of d hops. • To derive constructive lower bounds, use: • Geographic routing strategic along great circles • Greedy coloring schedules.

8. Per-node Capacity [Grossglauser & Tse] - Nodes are mobile [Francheschetti &Dousse] - Nodes static - Power control allowed • [Gupta & Kumar] • Nodes static • Interference model: protocol or physical model • Common power level across network Number of nodes Capacity scaling of ad hoc networks

9. Mobility can increase capacity • [Grossglauser & Tse] achieve constant capacity scaling by two-hop relaying • [Gupta & Kumar] allow for constant capacity scaling if the traffic pattern is purely local. • Source uses one of all possible mobile nodes as a relay. • Source splits stream uniformlyacross all relays. • When a mobile forwarder nears the destination, it hands off packet.

10. Mobility can increase capacity • Why does mobility increase capacity? • By choosing a random intermediate relay, the traffic is diffused uniformly throughout the network. • Thus, on average, every mobile node has a packet for every other destination and can schedule a packet to a nearby destination in every slot. • (For those who took randomized algorithms, this is akin to permutation routing algorithms) • Catch: forwarding strategy improves capacity at the expense of introducing delay. • Need to study the delay-capacity tradeoff!!

11. Main contributions • Delay-capacity tradeoff: increasing the maximum allowable average delay increases the capacity. • Delay-capacity tradeoff depends on network setting, mobility patterns. • Different mobility models have been studied in the literature • i.i.d • Brownian motion • Random way-point • Random walk • Difficult to compare results across paper because network setting are quite different. • How does the mobility model affect the delay capacity trade-off?

12. Main Results: Notion of critical delay to compare mobility modes • For each mobility model, there is a critical delay below which node mobility cannot be exploited for improving capacity. • Critical delay depends mainly on mobility pattern, not on network setting

13. Overview • Mobility can increase capacity. • Delay-capacity tradeoff depends on network setting, mobility models. • Some questions arises • How representative are these mobility models in this study? • Can the delay-capacity relationship be significantly different under the mobility models? • What sort of delay-capacity trade-off are we likely to see in real world scenario?

14. Main Results A new hybrid random walk model • Propose and study a new family on hybrid random walk models, indexed by a parameter in [0, ]. • For the hybrid random walk model with parameter ,critical delay is • As approaches 0, the hybrid random walk model approaches an i.i.d mobility model. • As approaches , the hybrid random walk model approaches a random walk mobility model.

15. Critical Delay random walk model Hybrid random walk model i.i.d Number of nodes Main Results A new hybrid random walk model 1

16. Main Results A new hybrid random direction model • Propose and study a new family on hybrid random direction models, indexed by a parameter in [0, ]. • For the hybrid random direction model with parameter , the critical delay is • As approaches 0, this hybrid random direction model approaches a random way-point model. • As approaches , this hybrid random direction model approaches a Brownian mobility model.

17. Critical Delay Brownian mobility Hybrid random direction model Random Way-point Number of nodes Main Results A new hybrid random direction model 1

18. The Models

19. Hybrid random walk model • Divide the unit square into cells of area • Divide each cell into sub cells of area • In each time slot, a node is in one of sub cells in a cell. • At the beginning of a slot, node jumps uniformly to one of the sub cells of an “Adjacent cell”

20. i.i.d mobility model • As approaches 0, we get i.i.d mobility. • One big cell with n sub-cells. • In each slot, a node is in one of the sub-cells. • At the beginning of a time slot, a node jumps uniformly to one of the n subcells.

21. Random walk model • As approaches , we get the random walk. • n cells, one sub-cell in each cell. • In any slot, a node is in particular cell. • At the beginning of a slot, node jumps uniformly to one of the adjacent cells.

22. The average neighborhood size scales as Hybrid random direction model • Motion of a node is divided into trips. • In a trip, node chooses a direction in [0,360] and moves a distance • Speed of movement (for scaling reasons).

23. Discrete random direction model. • Divide the square into cells of area tours of size • Time divided into equal duration slots • At the beginning of a slot, a node jumps uniformly to an adjacent cell. • During a slot, the node chooses a start and end point uniformly inside the cell, and moves from start to end. • Velocity of motion is made inversely proportional to distance.

24. Brownian motion mobility • For , the discretized random direction model degenerates to the random walk discrete equivalent of a Brownian motion with variance

25. Critical delay and 2-hop delay

26. Definition of critical delay • We know that in the static node case, per node capacity is . Capacity achieving scheme is the multi-hop relaying scheme of Gupta & Kumar. • If mobility is allowed, the two-hop relaying strategy achieves per node capacity of [Grossglauser & Tse] • The two hop relaying strategy has an average delay of , under most mobility models. • Mobility increase capacity at the expense of delay.

27. Definition of critical delay (conti) • Suppose we impose the constraint that the average delay can not exceed . • Under this constraint, relaying strategy that use mobility will achieve a capacity , somewhere between and • For some critical delay bound , this capacity will be equal to capacity of static node networks. • Below this critical delay , there is no benefit from using mobility based relaying.

28. [Grossglauser & Tse] 2 hop relaying scheme has been shown to incur an average delay of about under many different mobility models [Gupta & Kumar] Critical delay is the minimum delay that must be tolerated Two hop delay Critical delay An illustration of critical delay Capacity Maximum average delay

29. More on the critical delay • It depends on the mobility mode. • It provides a basic to compare mobility model. • If mobility model A has lower critical delay than mobility model B , then A provides more leeway to achieve capacity gains from mobility than B. • Critical delay also depends on what scheduling strategies are allowed.

30. Critical Delay and 2-hops Delay Under Various Mobility Models

31. Lower bound on critical delay for hybrid random walk models • Obtain a value such that if average delay is below this value than (on average) packets travel a constant distance using wireless transmissions before reaching their destinations. For the hybrid random walk model , this value is • Show that if packets are on average relayed over constant distance using wireless transmission, this results in a throughput of ,with the protocol model of the interference. • Thus, the critical delay can not be any lower than this value.

32. Lower bound on critical delay for hybrid random walk models (cont) • Step1: Establish a lower bound on the first exit time from a disc of radius • Step2: If average delay is smaller than , than packets must on average be relayed over a distance no smaller than • Pigeonhole argument • Exit lemma • Union Bound • Motion arguments for successful relaying.

33. Upper bound on critical delay for hybrid random walk models • Develop a scheduling and relaying scheme that provides a throughput of while incurring a delay of • Consider a scheme where relay node transfer the packet to destination when it is in the same cell as destination • Delay=(approx) time for delay node to move into destination node’s cell. • Packet arrivals are independent of mobility delay is the same as mean first hitting time on a torus of size • This first hitting time=

34. Upper bound on critical delay for hybrid random walk models (conti) • With this strategy, multi-hop relaying is only used once we reach the destination’s cell, ie., at most distance • Each hop travels a distance • Throughput loss from multihop relaying = • Since each wireless transmission travels ,nodes within this range must stay silent. • An additional throughput loss of • Combining the two, throughput=

35. Discussion on hybrid random walk models • As increases, the critical delay increases, thereby shrinking the delay-capacity trade-off region. • Two extreme cases: • i.i.d model: when the static node capacity can be achieved even with a constant delay constraint. • Random walk model: where delay on the order of is required to achieve the static node capacity.

36. Lower bound on critical delay for hybrid discretized random direction models • Same approach as before to obtain lower bound on critical delay as • Step1: derive a lower bound on exit time from a disc of radius 8 under the random direction model • Step2: If average delay is smaller than packets must on average be relayed over a distance on smaller than

37. Upper bound on critical delay for hybrid discretized random direction models • Same strategy as before • Replicate and give to relay node • Relay node hands off to destination when it is in the cell of the destination • Can obtain a throughput of with a delay of • Provides an upper bound on critical delay for discreted random direction model.

38. Discussion

39. Discussion : Characteristic path length • Critical delay seems to be inversely proportion to characteristic path length of a mobility model. • Characteristic path length is the average distance traveled before changing direction under the model. • For example, with hybrid discretized random ditection model, characteristic path length is and the critical delay is

40. Discussion : Characteristic path length(cont) • Thus, a scenario with nodes moving long distance before changing direction provides more opportunities to harness delay-capacity trade-off, e.g., random way point model vs. Brownian model.

41. Conclusion

42. Conclusion • Motivate capacity-delay tradeoff in MANET（Mobile Ad-hoc NETworks ）. • Define critical delay to compare capacity-delay tradeoff region across mobility models. • Define a parameterized set of hybrid random walk models and hybrid random direction models that exhibit continuous critical delay behavior from minimum possible to maximum possible.

43. Q&A感謝各位聆聽Thanks for your Listening