Matthew AndrewsBell Labs

Joint with Lisa Zhang

February 16, 2006

Theory of Mobile CommunicationTheory of Mobile Communication

• 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

Background

• Some areas of wireless research where TCS ideas are useful

• A few interesting open problems

Overview of talk

• 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

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

Some areas of interest

38.4kbps?

Wireless scheduling

614.4kbps?

• 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)

Wireless data scheduling model

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

data arrival process

DRCi (t)

DRCj (t)

t

service rate vector(DRC1(t),…,DRCn (t))

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

Mobility

• Mobility destroys stationarity

DRCi (t)

service rate vector(DRC1(t),…,DRCn (t))

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

One interesting question

• Max Weight (See Tassiulas-Ephremides, Kahale-Wright, Neely-Modiano-Rohrs, Stolyar) – qi(t) = queuesize of user i at time t – Serve argmaxi qi(t) * DRCi(t) – For stationary channels

– Potential function i qi(t)2 has negative drift

– Queues remain stable – For adversarial channels

– ??????

• 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

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?

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?

Routing

• 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)

Congestion Control

• 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”

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

Congestion Control as Network Utility Maximization

• 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

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?

Congestion Control + Scheduling xp’xp

• 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?

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?

Capacity Analysis

• In a wireless network:– Should my address say who I am or where I am?

– How do geographic addresses affect routing?

Addressing

locale