1. Mobility Increases Capacity In Ad-Hoc Wireless Networks Lecture 17 October 28, 2004 EENG 460a / CPSC 436 / ENAS 960 Networked Embedded Systems & Sensor Networks Andreas Savvides andreas.savvides@yale.edu Office: AKW 212 Tel 432-1275 Course Website http://www.eng.yale.edu/enalab/courses/eeng460a

2. Today: Two Different Aspects of Mobility  Communication: Capacity of Mobile Networks M. Grossglauser and D. Tse, “Mobility Increases the Capacity of Wireless Ad-Hoc Networks”, Proceedings of INFOCOM 2001  Sensing & Coordination: Constrained Mobility – Anjan’s Presentation

3. Introduction: Capacity in Mobile Networks  Channel variations in time in wireless networks Multipath fading Path-loss through distance attenuation Shadowing by obstacles Interference from other users  How to cope with channel variations Use diversity oOver time - interleaving coded bits oFrequency diversification oSpace – multiple antennas –Multiple independent signal paths between a sender and a receiver

4. Motivation  Exploit time-scale channel fluctuations in time Multiuser diversity – frequent topology changes due to user mobility  Focus on asynchronous applications Users don’t care about end-to-end delays oe.g email, data sysnchronization between a mobile terminal and an application, some types of event notification  Show that the theoretical network capacity increases with mobility

5. Consider Static Networks First  Gupta & Kumar Result The Capacity of Wireless Networks, IEEE Transactions on Information Theory, March 2000  Proposed model for studying the capacity of wireless networks Fixed ad-hoc network, randomly deployed nodes Each node has a random destination it wants to communicate  Main Result: As number of nodes n per unit area increases, the throughput per source destination paper decreases approximately like 1/√n  Results indicates best performance achievable Optimal scheduling, routing and relaying Pessimistic result – traffic rated per sender-destination pair goes to 0!

6. This paper Mobility as a source of multi-user diversity: Average throughput of sender-destination (S-D) pair can be kept constant as number of nodes per unit area n increases Caveat, long term throughput averaged over the node mobility time-scale => delays of the same order can occur Distribute packets to as many nodes as possible oMobile relay nodes, temporarily buffer a packet and pass the packet to destination when they come close to it

7. Fixed vs. Mobile  Fixed nodes Long range communication between multiple S-D pairs limited by interference Communication needs to take place between nearest neighbors oDistances of 1/√n oMultiple hops to destination - √n oActual useful traffic per pair is fairly small  Mobile nodes Transmit only when nodes are close together Use at most 1 relay node

8. Signal to Interference Ration (SIR) Model Channel gain Background noise power Transmit power of node i Processing gain: 1-spread spectrum, >1 CDMA SIR for successful communication Positions for nodes (i,j)

9. Assumptions  Results are based on an idealized setup  Assume a central scheduler At time t, scheduler chooses the senders and their power levels  Goal: under random motion patterns Show that the long term throughput remains constant as the number of users increases

10. Mobile Nodes w/o Relaying  Can mobile nodes achieve a throughput of O(1) per S-D pair by not relaying at all?  Answer: number of simultaneous long range communications is limited by interference Positions of nodes t,j at time t S(t) – Set of source nodes that are scheduled for successful transmission

11. Mobile nodes without relaying  Without relaying the achievable throughput per S-D pair goes to 0 at least as fast as Distance attenuation factor

12. Mobile nodes with relaying  What is the problem with direct transmission to S-D pairs? Transmissions are long range => interference limits the number of concurrent transmissions  How can we increase throughput? Constrain transmission to nearest neighbors oUse lower transmission power to avoid interference Cannot wait for nearest neighbor to come close by, time 1/n – vanishes at time goes by

13. Mobile nodes with relaying  Spread out packets along a large number of relay nodes Nodes temporarily buffer packets while they move Ensure that every node will have packets to send to its nearest neighbor at any time oNote you cannot do this with direct transmission alone!

14. Scheduling Policy & Theorem 3.4  Assume that time is divided into slots  Fix a sender density parameter  Select the sender receiver pairs where the interference is small enough to make transmission possible  Theorem 3.4 The number of feasible sender- receiver pairs is O(n) Proof based on interference analysis not shown here

15. 2-phase scheduling policy Apply a 2-phase interleaved scheduling policy: 1)Souce sends to relay (odd slots) 2)Relay sends to destimation (even slots) Direct transmission to destination is also allowed if destination is close enough

16. 1 hop vs. 2-hop routes Theorem 3.4: Number of feasible sender receiver pairs is O(n)  The long-term throughput between any two nodes is equal to the probability that 2 nodes are a feasible node pair O(1/n) according to the theorem  Throughput over direct route O(1/n)  Single hops routes alone O(1/n)  In 2-hop routes there are n-2 routes  Total average throughput per S-D pair is O(1)

17. Main result of the paper Theorem 3.5: The two-phased algorithm achieves a throughput per S-D pair of O(1) i.e there exists a constant c>0 such that

18. Numerical Results

19. Note performance degradation at large thetas

20. Conclusions/Summary  Mobility can increase capacity is delay can be tolerated Email, synchronization and data collection applications would be good candidates Not useful for cellular telephony oDelays cannot be tolerated  Remember: Gupta & Kumar result Capacity scales with 1/√n  Result under mobility assumptions in this paper Capacity O(1)