Distributed resource allocation in wireless data networks: Performance and design Alexandre Proutière Orange-FT / ENS Paris.

Distributed resource allocation in wireless data networks:Performance and design

Alexandre Proutière

Orange-FT / ENS Paris

Outline

Modelling the Internet at flow level Capacity region Rate regions (throughput regions)

Distributed resource allocation in wireless data networks: issues and problem formulation

Rate regions for distributed scheduling Systems without information exchange: the mean field

approach Applications

Outline

Modelling the Internet at flow level Capacity region Rate regions

Distributed resource allocation in wireless data networks: issues and problem formulation

Rate regions for distributed scheduling Systems without information exchange: the mean field

approach Applications

The internet is a flow-level queue

A set of resources shared by a varying number of elastic connections (flows)

QoS: Time to transfer a flow (or flow throughput)

Randomly varying population of flows

Flows randomly generated by users, cease upon transfer completion

Flows of the same class require the same set of resources

Class k flows Mean flow arrival rate per second

Mean size bits Traffic intensity bit/s

The capacity region

Flows are transferred in a finite time, iff the process of the numbers of flows is stable

Capacity region: the set of such that the network is stable at flow-level

(The capacity region quantifies the network provider revenues)

Static population – rate regions

Fix the numbers of flows of different classes

Rate region = set of feasible long term rates of flows of the different classes The long term rate vector is feasible if there exist packet

level mechanisms realizing this rate vector and stabilizing all queues in the network

Packet level mechanisms: resource allocation schemes + congestion control algorithms

Packet level mechanisms

The type of considered networks defines some constraints on packet-level mechanisms Resource allocation in CDMA nets: no time sharing Congestion control algorithms based on losses: at least one

buffer per route must be saturated – the greedy behaviour of TCP

… In wireless networks with distributed scheduling, this greedy behavior reduces the rate region

Rate regions - wireless networks

Slotted ALOHA - two interfering links

1 slot = 1 packet

With or without greedy congestion control

Rate regions - wireless networks

CSMA/CA - two interfering links

Without greedy congestion control

Rate regions - wireless networks

CSMA/CA - two interfering links

With greedy congestion control

The realized resource sharing

The rate vector in each network state belongs to the rate region and is defined by the set of chosen packet level mechanisms:

Example: F. Kelly, schemes designed so as to maximize some network utility

From rate regions to the capacity region

A rough theorem* Consider a system where we are able to characterize the allocation in all states. Define .Then the system is stable at flow-level ifThe converse is true if is convex.

NB: is the largest coordinate convex set containing the contour of

Rate regions Capacity region *true for K = 2, ongoing work in higher dim

The big picture

Flow-level traffic demand

Multi-class queuewith state-dependent capacity

Packet level dynamics: rate regions

Capacity regionFlow-level performanceObjective

Design

Outline

Data network modeling Rate regions Flow-level dynamics

Distributed resource allocation in wireless data networks: issues and problem formulation

Rate regions for distributed scheduling Systems without information exchange: the mean field

approach Applications

Wireless resources

Bandwidth Power Time Space Fading …

time

power

Wireless resources

Bandwidth Power Time Space Fading …

time

power

A single channel shared by active links in time/power

Link rate vs. SINR

Fixed-rate systems SINR

Adaptive variable-rate systems

rate

SINR

Requires the use of rate adaptation techniques

Decision elements

Information at the transmitter

Buffer contentSINR (estimation)The past

Information that can be shared

Intention to transmit Transmission powerBuffer contentSeeds (random access)…..

Distributed systemsThe rate/information tradeoff

sig packetfailure time

packet transmission

Distributed systemsThe rate/information tradeoff

1. For a fixed set of shared information, what is the distributed resource sharing scheme leading to the largest capacity region (flow-level perf.)?

Distributed systemsThe rate/information tradeoff

2. What is the distributed resource sharing scheme leading to the largest capacity region? What info do we need to realize that?

From Tassiualas-Ephremides … … to Modiano, Shah, Zussman

A scheme achieving max rate when exchanging the queue lengths within connex components of the graph of schedule

Thru unknown …

State-of-the-art

What is the maximum capacity region of distributed systems without any signaling? When users play with time and power only (they decide

when and at which power to transmit)

Today …

Outline

Data network modeling Rate regions Flow-level dynamics

Distributed resource allocation in wireless data networks: issues and problem formulation

Rate regions for distributed scheduling Systems without information exchange: the mean field

approach Applications

Mean field for random multi-access algorithms

A fixed number of saturated sources Fixed rate system All links are interfering with each other Each node runs a random multi-access algorithm

(e.g. exponential back-off algorithm)

System state evolution

All nodes share the same "slot point process"empty slot

collision

successful trans.

The slot point process

System state evolution:

System state evolution (cont'd)

Example 1: Exponential back-off algorithm (DCF)

Issue: Analyzing the Markov chain is not possible…

Example 2: Impatient Back-off Algorithm*

* R. Gupta, J. Walrand 2005

The mean field asymptotics

Idea: let the number of sources be large, and see … Renormalization: Trajectories (instead of marginals): Use Sznitman's propagation of chaos to prove asymptotic

decoupling:

The processes of back-offs of the various sources are almost independent*.

* A heuristic used by G. Bianchi 2000, it works for N=3!

Propagation of chaos

Theorem 2

Evolution of marginals

Theorem 3

A stable dynamical system!

Stationary regime

Theorem 4Same results hold in stationary regimes. The system is decoupled, and the stationary behavior of the system can be explicitly characterized

Example: Exponential back-off algorithm

Extensions

Non-saturated sources Power control (instead of time control) Systems with partial interaction … All systems where no information is exchanged?

Coupled vs. decoupled systems

Ideal scheduling schemes lead to coupled systems

decoupled coupled

*A proof via mean field

Outline

Data network modeling Rate regions Flow-level dynamics

Distributed resource allocation in wireless data networks: issues and problem formulation

Rate region for distributed scheduling Systems without information exchange: the mean field

approach Applications

Performance of existing systems

The mean field principle provides explicit asymptotic performance results (e.g. rate regions)

Example: Rate region of fixed ALOHA systems

Stability unknown and sensitive.The DP provides good approximation of the stability condition.

*An open problem for 30 years

The limit

A set of links interacting with each other One slot = one packet

The feasible set of rate vectors achievable without information exchange is:

If fairness is imposed the global throughput does not exceed

Design of optimal systems

Proportional fairness in single hop networks

Decoupling principle

*See Kar et al., Gupta-Stolyar

What about power control?

Fixed rate systems, tuning power… … impacts the network connectivity in ad-hoc networks Clear incentives to tune power

Variable rate systems Does implementing a distributed power control scheme

make sense?

The decoupling principle says that thescheme results in stationary powers depending of the number of flows on each link ( e.g. the scheme cannot emulate time-sharing)

Rate regions (single hop nets)

Power limitation:

SNR:

Max Power policy

We compare the capacity region of smart power control policies with that obtained with the "stupid" max power policy (I transmit with full power when I have a packet)

Playing with power reduces the capacity region

Well … worse scenario for me …

30m 52m 30m

802.11a channelsP = 100mW

No more than 7% better thanthe max power policy!

Summary

We derived a general model to evaluate the performance of data networks

Accounting for user dynamics is crucial! We applied the model to networks with distributed

resource allocation The rate region of such networks is unknown in

general When no information is shared, the decoupling

principle allows to compute the rate region, to compare different approaches

Summary / Perspectives

The DP allows to easily identify the best performance one can obtain without sharing information.

What capacity gain when exchange traffic information?

What information do we need to share to obtain some desirable coupling? Need new math models to study coupled systems

?

Thanks!

http://perso.rd.francetelecom.fr/proutiere