Peter Key Cambridge UK

http://research.microsoft.com/network/disgame.htmjoint work with

Richard Gibbens,Statistical Laboratory, Cambridge Uni. UK

The Use of Games for assessing user strategies for differential

QoS in the Internet

Outline

Background Congestion Pricing A File Transfer Game

Access to / Control of Scarce Resources Users and the Network have different

objectives … So why not use the right signals to

encourage cooperation? Signals reflect congestion costs

Send a signal to users when traffic that should not be carried enters (moveable threshold)

The ECN bit could be used to carry the information

Theory & Background Work of Kelly et al, has shown users’

optimum converges to System Optimum (maximum welfare) with right marking scheme. Related work by Low etc

Gibbens & Kelly put in a Congestion pricing framework

Architecture & experiments in Key et al.

Network vs Users

“My work is a game, a very serious game”Escher

Users

Signals

Data/Info

Network

Distributed Multi-player Game

Internet

MSRCambridge

Game server

Players

Example Game

Transfer a given amount of data F at minimum cost in time T, maximum rate P eg F=1000pkts, T=100s, P=20pps

Background load of 100 WTP users alternating on and off periods (10 & 30 s) Willing to pay different amounts

600 pps bottleneck link (eg 5Mb/s) shadow queue marking (threshold 9, cap 540

pps) Repeated runs

WTP background users ‘Willing-to-pay’ an amount w per

unit time Elastic users — adjust rate of

sending to keep marking rate close to w

Defines a packet-send strategy

Background Load

Arrival rate

050

100150200250300350400450500550600

50 70 90 110 130 150 170 190

Time (s)

pp

s

Marking periods

0

2

4

6

8

10

12

14

16

18

20

60 61 62 63 64 65

Time

Bu

ffer

Shadow queue Real queue

0

1

2

3

4

5

6

7

8

9

10

60 61 62 63 64 65

Time

Bu

ffe

r

A baseline Strategies

CBR : send at constant rate If in stationary regime, this is an

optimal strategy if price function “convex” in region wrt

load (lightly loaded) and prices iid, or a Martingale

A last packet strategy (like tit-for-tat) Use feedback to dynamically

adjust rate If (last packet not marked

/dropped) {send at high rate = peak rate } else

{send at low rate}

A variant is …

A last-2 packet strategy Attempts to determine non-

marking periods If (last 2 packets not marked

/dropped) {send at high rate = peak rate } else

{send at low rate}

Estimation Algorithms Use a Statistical procedure to estimate

trends Eg attempt to estimate p(mark)

eg use a Bayesian update based on last n packet history

send rate related to

More complex algorithms attempt to estimate marking/non-marking periods

pp

ˆ1

or ˆ1

Sending rates example

0

100

200

300

400

500

600

700

800

900

1000

50 70 90 110 130 150

Time

Pa

ck

ets

Last 2

Last 1

Constant rate

Estimator

Marks

Results for high load, T=100

0

50

100

150

200

250

300

0 50 100 150 200 250

Constant

last 1

last 2

estimate

Raw FTP sends in 5 seconds, cost 410

Start seed

Marks

Results for high load, T=100

Raw FTP sends in 5 seconds, cost 410 time to complete

Marks

Marks vs Time

0

50

100

150

200

250

300

50 60 70 80 90 100

Constant Rate

Last-1

Last 2

Esimate

Results for high load, T=10

Raw FTP sends in 5 seconds, cost 410 time to complete

Marks

0

50

100

150

200

250

300

350

400

450

0 5 10 15

Constant Rate

Last-1

Last 2

Esimate

Conclusions Experiments suggest simple strategies

are powerful (cf Axelrod’s work) Simulation environment with ‘game

playing’ enables strategies to be compared and developed

Future work will look at different and mixed objectives

The Internet is a non-cooperative game, but the right signals can encourage effective cooperation