Matthew Andrews Bell Labs Joint with Lisa Zhang February 16, 2006

1. Theory of Mobile Communication Matthew Andrews Bell Labs Joint with Lisa Zhang February 16, 2006

2. Background • The internet is going mobile • Wifi, 3G cellular, picture phones, PDAs, ad-hoc networks • Optimization is important • Spectrum is limited and expensive • No equivalent of “putting in another fiber” • Need to maximize use of available resources • Problems are hard • Dynamically changing environments • Many interactions between users

3. Overview of talk • Some areas of wireless research where TCS ideas are useful • A few interesting open problems

4. Some areas of interest • Scheduling • Routing • Capacity Analysis • Congestion Control • Addressing • Exists a lot of work on wireless problems • Vast majority is average case analysis • What can TCS provide? • Many tools for worst-case analysis

5. Some areas of interest • Scheduling • Routing • Capacity Analysis • Congestion Control • Addressing • Is worst case analysis important in wireless networks? • No real justification for many statistical assumptions made • “The most important thing to know about a system is how it breaks” P. Fleming, Motorola

6. Wireless scheduling 614.4kbps? 38.4kbps? • Choose queue/user • Serve distant user at 38.4kbps or close user at 614.4kbps • Service rates user dependent!!!! • Service rates change over time!!!! • (user mobility, channel fading)

7. Wireless data scheduling model data arrival process DRCi (t) DRCj (t) t service rate vector (DRC1(t),…,DRCn (t)) • Choose a queue/user to serve at time t • If we choose user i, serve at rate DRCi (t) • Opportunistic scheduling: Serve user when DRC is high

8. How do we model the channel? Channel model 1: Stationary stochastic process • Service rate vector determined by state of ergodic Markov chain M • M(t)  (DRC1(t),…,DRCn (t)) • Most of the literature works in this model service rate vector (DRC1(t),…,DRCn (t))

9. Mobility • Mobility destroysstationarity DRCi (t)

10. How do we model the channel? Channel model 2: Adversarial process • Service rate vector determined by adversary • Adversary wants scheduler to do bad things • Adversary enables worst-case analysis service rate vector (DRC1(t),…,DRCn (t))

11. One interesting question • Max Weight (See Tassiulas-Ephremides, Kahale-Wright, Neely-Modiano-Rohrs, Stolyar) • qi(t) = queuesize of user i at time t • Serve argmaxiqi(t) *DRCi(t) • For stationary channels • Potential function i qi(t)2has negative drift • Queues remain stable • For adversarial channels • ??????

12. Routing • Three types of routing • Source Routing • Source computes entire route to destination • Useful for traffic engineering, QoS enforcement, protection (disjointness) etc. • Hop-by-hop Routing • Send data to neighbor that’s advertising good route to dest • Good for Shortest Paths • Queue-based Routing • Each node maintains per-dest queue • Send data to neighbor that has short queue

13. Routing • Some interesting routing questions • What type of routing is most appropriate for dynamic wireless networks • How do we do traffic engineering, disjoint paths etc. in dynamic graphs? • What is best way to compute shortest paths in wireless networks? • How much of dynamic graph literature can be applied? • Interested in communication overhead rather than amortized running time • Need to be aware of traffic matrix • Proactive vs reactive routing • Are standard routing algorithms (e.g. AODV, OLSR) optimal?

14. Routing • Some interesting routing questions • Queue-based routing • Awerbuch-Leighton, Aiello-Kushilevitz-Ostrovsky-Rosen • “Queue-based routing algorithms are throughput-optimal in static networks” • What about dynamic wireless networks? • Anshelevich-Kempe-Kleinberg, Awerbuch-Berenbrink-Brinkmann-Scheideler • Optimality holds for single-sink problem • What about general multicommodity case?

15. Congestion Control • TCP has well-known problems in wireless networks • Packet loss due to interference is perceived as congestion • Fixes: • Snoop protocol ( Balakrishnan, Seshan, Amir, Katz) • Split connections • Loss prevention: FEC, HARQ, DARQ, link-level retransmissions • Buffer sizing is difficult • Buffer size should equal bandwidth-delay product (BDP) • In wireless networks BDP varies due to variable link rate • Leads to excess buffering (>30s buffering in one study)

16. Congestion Control as Network Utility Maximization • Wireline networks max Up(xp) subject to . e p xp  ce • xp = inj rate on path p • ce = capacity of edge e • Up(.) = utility function (e.g. log) • Kelly-Maulloo-Tan, Low-Lapsley, Low-Peterson-Wang… • “TCP is a primal dual algorithm for solving above problem”

17. Congestion Control as Network Utility Maximization • Wireless networks max Up(xp) subject to . ( …, xp , … ) C • C = system capacity region (convex) • Depends on power assignments, interference etc. • Chiang • Joint power control and congestion control for solving problem

18. Congestion Control + Scheduling xp xp’ • Wireless networks max Up(xp) . subject to . ( …, xp , … ) C . • Stolyar, Srikant • Joint congestion control and scheduler for solving problem • Why is joint congestion control and scheduling important? • Need complex scheduler to realize capacity region • Don’t want scheduler to try and serve empty queue • Want large queue to backpressure to source to prevent excess queueing

19. Congestion Control + Scheduling xp xp’ • Wireless networks max Up(xp) . subject to . ( …, xp , … ) C . • Question: • Previous work on congestion control + scheduling is for stationary wireless channels • What about adversarial channels?

20. Capacity Analysis • Gupta-Kumar • In an n-node ad-hoc networks • Throughput per source-dest pair is O(1/n log n) • Grossglauser-Tse, El Gamal et al • Throughput per source-dest pair is O(1) if nodes move • In this work • Traffic patterns, node distributions and mobility are uniform • How can we evaluate capacity for arbitrary inputs?

21. Capacity Analysis • Optimization problem • Fixed set of transmitters and receivers • Transmission is successful if Signal-to-Noise Ratio is above threshold • Choose powers to maximize aggregate system throughput • How hard is this problem? • Does it get easier if throughput is weighted by queue length?

22. Addressing • In a wireless network: • Should my address say who I am or where I am? • How do geographic addresses affect routing? locale