Optimal Resource Allocation in Overlay Multicast

1
Optimal Resource Allocation in Overlay Multicast

• Yi Cui, Yuan Xue, and Klara Nahrstedt
• University of Illinois at Urbana-Champaign
• University of Toronto
• yicui, xue, klara_at_cs.uiuc.edu

2
Introduction

• Overlay Multicast

S
S

h1
h1
h2
h2

h3
hN
h3
hN

• Advantages
• Easy Deployment
• Supporting Multi-rate multicast

3
Challenges
S
S

h1
h1
h2
h2

h3
hN
h3
hN

• Goal
• Maximizing Overall Utilities of all Receivers
• Constraints
• Network Capacity Constraint
• Data Relay Constraint

4
Our Contributions

• Theoretical Foundation
• Non-linear Optimization Model
• Unicast F. Kelly, S. Low
• IP Multicast K. Kar and S. Sarkar
• Pricing Scheme
• Protocol Design
• An end-host-based Rate Adaptation Protocol

5
Network Model
0
f1
f2
2
1
f3
Goal Maximize
3
f4
f5
4
5
0
3
10
6
3
15
2
Network Constraint
4
1
R1
R2
8
2
5
2
3
0
Data Constraint
4
1
R1
R2
5
2
6
A Price-based Approach

• Lagrangian form

maximizer
Path Price
Relay Benefit
All edges along the path of
All children of
Link Price
Relay Price
7
Example
0
f1
f2
2
1
f3
3
f4
f5
4
5
0
3
Path Price
l1
l5
Relay Benefit
l2
l4
l6
4
1
R1
R2
l3
l7
5
2
3
0
4
1
R1
R2
5
2
8
Algorithm

• Rate adaptation and price calculation
• Link Price Update
• Relay Price Update k
• Flow Rate Adaptation
• Convergence
• The algorithm converges to the unique optimal
  point

Supply and demand relation
All flows traversing
Supply and demand relation
is the parent of
9
Example
0
f1
f2
2
1
f3
3
f4
f5
Optimal Value
4
5
0
3
Optimal Rate Allocation
10
6
3
15
2
4
1
R1
R2
8
2

• If we treat them as independent flows

5
2
Optimal Value
3
0
Optimal Rate Allocation
4
1
R1
R2
5
2
10
Protocol Link Delegation
LPU
FRR
3
C (1, 2)
C (3, 4, 5)
LPU
FRR
C (3)
R1
R2
4
1
C (4)
C (1)
LPU
FRR
FRR
LPU
C (5)
C (2, 3)
5
2

• FRR Flow Rate Report
• LPU Link Price Update

11
Protocol Aggregate Route Pricing
FRR
3
C (1, 2)
C (3, 4, 5)
FRR
FRR
C (3)
R1
R2
4
1
C (4)
C (1)
FRR
FRR
C (5)
C (2, 3)
5
2

• FRR Flow Rate Report

12
Evaluation

• Simulation setup
• BRITE Topology Generator
• 10 ASes, each with avg. 100 nodes
• Bandwidth Distribution 10 100 Mbps

13
Convergence

• Update Interval 0.1 second

14
Average Messaging Overhead
15
Conclusion and Future Directions

• Concluding remarks
• A pricing-based algorithm maximizing the
  aggregate utilities of all receivers
• An end-host based protocol
• Future direction
• Faster convergence under asynchronous messaging
  paradigm
• Implicit Link Price Update