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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
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