Mobile Ad hoc Networks COE 549 Delay and Capacity Tradeoffs II

1. Mobile Ad hoc Networks COE 549 Delay and Capacity Tradeoffs II Tarek Sheltami KFUPM CCSE COE www.ccse.kfupm.edu.sa/~tarek

2. Outline • Multi-user in Mobile Network • Static vs. Mobile Ad Hoc Networks • Direct Contact vs. Simple Replication • Why multi-hop relaying in static networks? • Tradeoff between delay and capacity

3. Typical Scenario • n nodes communicate in random S-D pairs • All nodes are mobile, no fixed base station • Applications are delay tolerant • Email • Database Synchronization • Control message to Explorer on Mars • Topology may change during packet delivery

4. Multi-user in Mobile Network • Direct contact: • The source holds the packet until it comes in contact with the destination • Minimal resource, but • long delay • This idea is very simple, but does not perform very well. In fact, any scheme that does not use relaying can not do better than: • Where is the minimum simultaneously successful transmissions

5. Scheduling Policy • We slot time, and index slots by t. • In each slot, each node transmits with probability • Each transmitter transmits to its closest neighbor • There will be a lot of collisions: • The expected number of successful receptions Nt is on the order of n: • With n nodes, it is possible to have around successful transmissions, with S/N requirements

6. Multi-user in Mobile Network • Simple replication: • S sends a replicate to as many different nodes as possible. These relays hand the packet off to D when it gets close • Each packet goes through at most one relay node  Higher throughput, relatively shorter delay

7. Methodology • Using the previous scheduling policy as a building block. • Nodes only transmit to their nearest neighbors. • In odd slots, each node transmits to its nearest neighbor a packet for its destination. • The neighbor will act as a relay. • In even slots, each node will relay to its nearest neighbor a packet destined for that node (if it has such a packet).

8. Multi-user in Mobile Network.. • Each of the n − 2 intermediate queues has arrival and departure rate equal to packets/slot • The link directly from the source to the destination has rate packets/slot. • The aggregate throughput per node is packets/slot

9. The Book Analogy • Imagine a large number of people moving around in a city • Each one carries a stack of books for a friend of his. The stack is very high • Whenever I bump on any other person on the street: • I either give him a book for him to give to my buddy, • or I give him a book that his buddy gave to me some time in the past • Chances that I bump on my own buddy are negligible • Question: What is the average number of people that their destinations are also nearest neighbors? This is related to the famous hat problem!

10. Model Assumptions • Session • Each of the n nodes is an S node for one session and a D node for another session • Each S node i has an infinite stream of packets to send to its D, d(i) • The S-D association does not change with time • Each node has an infinite buffer to store relayed packets • Central Scheduler • At any time t, the scheduler chooses which nodes will transmit which packet, and its power level

11. Transmission Model

12. Random Topology

13. Static vs. Mobile Ad Hoc Networks • When # of users per unit area n increases • Static: The throughput per S-D pair decreases approximately like • Long-range direct communication limited due to interference. • Most comm. has to occur between nearest neighbors • Distances of order • Hops to D of order • Actual useful traffic per pair is small • Best performance achievable with optimal scheduling, routing • Traffic rate per S-D pair can actually go to zero • Mobile:The avg. long-term throughput per S-D pair can be kept constant

14. Direct Contact vs. Simple Replication • Mobile Nodes w/ direct contact • Transmission are long range  interference prevents more concurrent transactions • For sufficient large N, throughput goes to 0 • Mobile Nodes w/ relaying (simple replication) • Overcame interference and distance limitation • Possible to schedule O(n) concurrent successful transmissions per time slot w/ local communication • Achieved a throughput per S-D pair of O(1)

15. Numerical Results

16. Receiver Centric Results

17. dIN d D S What is capacity here? • Not traditional information-theoretic notion • Notion of network capacity under interference • Modulation and coding scheme is fixed • In this notion of capacity, space is resource No other transmission in this area of

18. Capacity of static ad hoc networks • Gupta and Kumar [IEEE Trans. IT, 2000] • Uniform distribution of n nodes within a disk of unit area • Randomly chosen sender-destination pairs • Same power levelfor all transmissions • Per-node throughput as with multi-hop relaying • Agarwal and Kumar [ACM CCR, 04] • Per-node capacity of with power control

19. Why multi-hop relaying in static networks? • Direct transmission is bad • Transmission over distance d costs • Short transmission is better than long transmission • Multi-hop relay (via nearest neighbor) is best • Best possible is to transmit only to neighbors D hops D VS S S For each hop Required area = Required area = Network capacity = Network capacity = Per-node capacity = Per-node capacity =

20. Capacity of mobile ad hoc networks • Grossglauser and Tse [IEEE INFOCOM, 01] • Similar model as Gupta and Kumar, but with mobile nodes • Per-node capacity of is achievable with two-hop relay • Why two-hop relay in mobile networks? • Direct transmission cannot exploit mobility • More than two-hop decreases capacity

21. Per-node Capacity Grossglausser, Tse - Mobile nodes Number of nodes • Gupta, Kumar • Static nodes • Common power level Francheschetti, Dousse - Static nodes - Power control allowed Capacity scaling of ad hoc networks

22. What is ‘price’ for capacity? • Two ways to send a packet to D • Wireless transmission • Node mobility (=relay movement) • For given distance d between S and D • d = (sum of distances by transmission) + (sum of distances by relay movement) • To minimize first term is to maximize second term • Time taken for node mobility: Delay • Sum of distances by mobility results in time delay

23. Why tradeoff between delay and capacity? • Tradeoff between delay and capacity • d = (sum of distances by transmission) + (sum of distances by relay movement) • For capacity, reduce distances by transmission • For delay, reduce distances by relay movement • For given value of d • Can not reduce both distances!  tradeoff

24. D d Capacity S # of transmissions = 3 D R1 R2 S R2 R1 Illustration of tradeoff between delay and capacity • Assume appropriate scheduling • One transmission = distance of Total movement of relays = Delay

25. Critical Delay and 2-Hop Delay • Critical Delay: Minimum delay that must be tolerated under a given mobility model to achieve a per-node throughput of • 2-Hop Delay: Delay incurred by the 2-hop relaying scheme • The delay-capacity tradeoff exists for values of delay between critical delay and 2-hop delay

26. Hybrid Random Walk Models • The network is divided into n2β cells for β between 0 and ½ • Each cell is divided into n1-2 β sub-cells • Each node jumps from its current sub-cell to a random sub-cell in one of the adjacent cells • β=1/2 random walk model

27. Random Direction Models • Parameterized by β between 0 and ½ • Each node moves a distance of n-β with a speed of n-1/2in a random direction • Can pause for some time between steps

28. Lower Bound for Critical Delay • Main idea • If average delay is smaller than a certain value, packets travel average distance of to reach destination • Then show that this result in throughput of • HRW: Critical delay scales as • RD: Critical delay scales as

29. Calculating Critical Delay using Exit Time • Study exit time for a disk of radius r=1/8 centered at nodes initial position • Derive a lower bound on exit time that holds with high probability r = 1/8

30. Details of lower bound: Exit time • Let ςhrw and ςrd denote exit times for a disk of radius 1/8 in case of HRW and RD model with parameter β • Lemma (Lower Bound on Exit Time for HRW models): • Lemma (Lower Bound on Exit Time for RD models): C = slot duration

31. From Exit Time to Critical Delay? d 1 s r 1/4

32. Upper Bound for Critical Delay • Need to develop a scheme that achieves a throughput of • Delay can be upper bounded by first hitting time • for HRW models and for RD models

33. Summary of Main results • 2-Hop delay is roughly for all models • Critical delay scales as roughly for HRW models • Critical delay scales as roughly for RD models

34. Conclusions • Node mobility has strong impact on delay-capacity tradeoff • There exists minimum value of delay (critical delay) whichmakes capacity better than that of static ad hoc networks • Nodes change directions over shorter distances exhibit higher critical delay values • Nodes moving in same direction over longer distances shows a wider delay-capacity tradeoff