Andreas Savvides andreas.savvides@yale.edu Office: AKW 212 Tel 432-1275 Course Website http://www.eng.yale.edu/enalab/co

1. Mobility Increases Capacity In Ad-Hoc Wireless NetworksLecture 17 October 28, 2004EENG 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 • Over time - interleaving coded bits • Frequency diversification • Space – 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 • e.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 • Mobile 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 • Distances of 1/√n • Multiple hops to destination - √n • Actual 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 SIR for successful communication Transmit power of node i Background noise power Processing gain: 1-spread spectrum, >1 CDMA Channel gain 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 Positions of nodes t,j at time t S(t) – Set of source nodes that are scheduled for successful transmission • 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

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 • Use 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 • Note 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: • Souce sends to relay (odd slots) • 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. Numerical Results 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 • Delays cannot be tolerated • Remember: Gupta & Kumar result • Capacity scales with 1/√n • Result under mobility assumptions in this paper • Capacity O(1)