Greedy User Tuning for Rate Control
P. Ranjan,
Ranjan, E. H. Abed
Approach: Tune their utility function automatically using
washout filter-based feedback .
Rate Waveform without Control
ƒUser utility functions
U a ( x)
1
, a
a xa
p( y)
Rate waveform
User utility parameter
5
0
-Price elasticity of demand decreases with a
ƒResource price function
Queue
management
6
End-User Utility & Resource Price Function Design
b
y , b 0
Rate and Utility Parameter
Problem: How to automatically control greedy users in a
scalable manner?
4
3
2
ƒResponsiveness increases with b
1
0
ƒNetwork rate control system is stable regardless
of communication delay if
Mathematical Modeling (Kelly’s Framework):
ƒRate control problem formulated as a constrained
optimization problem:
maximize
U i ( xi )
i
subject to
Ax C
ƒProposed end-user algorithm:
x i (t ) k( wi (t ) xi (t ) pi (t ))
where wi (t )
s
G( s) =
, a>0
s+a
ƒWe can tune the utility parameter automatically
using washout filter-based feedback
xi (t ) U i' (t )
1000
1500
2000
2500
Time−>
3000
3500
4000
4500
5000
Rate and Utility Parameter Adaptation
b 1
1
a
ƒClearly, more elasticity in demand will
destabilize the system
ƒPeriodic orbit is generated via period doubling
bifurcation of the underlying map
ƒA washout filter is a stable high-pass filter with
transfer function
500
5
Rate waveform
Tuned utility parameter
4.5
4
3.5
Rate and Utility parameter
Feedback control:
Packet drop rate
0
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
0.8
1
Time−>
1.2
1.4
1.6
1.8
2
4
x 10
Rate waveform and user utility parameter in the
presence of controller
Conclusions:
1
2
server
N
Delayed
Feedback
Delay
Feedback
Control
Washout filter-based control schematics
1. Greedy users can be controlled in a scalable
manner by adaptively changing the shape of
their utility functions
2. Better performance in the presence of
aggressive users
3. Shielding of less aggressive users
4. Control does NOT modify the original
operating point