1

TDMA Scheduling in Competitive Wireless Networks

Mario Cagalj Hai Zhan

EPFL - I&C - LCA

February 9, 2005

2

Presentation outline

• Introduction• System model and problem statement• Proposed solution - Waterfilling Algorithm• Simulation results• Conclusions

3

Introduction

• Network nodes are owned by selfish users• Non-cooperative behavior of users (nodes)

results in a network collapse– e.g., with CSMA/CA MAC protocols the nodes can

cheat with their contention window to increase their throughput

• Our goal in this work:– to avoid bad outcomes by finding a better solution to

the channel allocation problem (a solution strictly preferred by each user)

4

System model

• We consider a general topology wireless network – hidden terminals are possible

• Nodes share a single communication channel• Traffic model:

– single-hop communication between K pairs of nodes– communicating peers always have packets to transmit

• TDMA-based MAC protocol• We use a link-based network model

5

Example 1: network topology

link 1

collision domain 1

collision domain 2

link 3

link 2

link 5

link 6

link 4

6

Example 1: link-based model

link 1

maximal clique 1

maximal clique 2

link 2link 3

link 5 link 6

link 4

7

Problem Statement

• Find an optimal capacity allocation that satisfies the following properties: – fairness (each link gets a fair portion of the system

capacity)– system optimality (wasted capacity is minimized)– uniqueness of the link-throughput allocation

• Find a TDMA scheduling that achieves the optimal capacity allocation

8

Capacity allocation problem

2 1

4 3

5

link -based model

q1 q2

q3

q4

q5

9

Example 2: capacity allocation

2 1

4 3

5

link -based model

q1 q2

q3

q4

q5

10

Challenges in general networks

• Problem: in general it is hard to find all relevant constraints

• In addition, it is hard to find all maximal cliques and the system capacity– determining the system capacity is equivalent to findin

g the maximum independent set (an NP-complete problem)

– the number of maximal cliques is exponential in the number of nodes in the link-based model

11

Waterfilling interpretation

• Simultaneously increase the rate of each link until some constraint(s) becomes binding

12

Waterfilling-based TDMA scheduling

• Since it is hard to solve the optimal capacity allocation problem, we approximate it

• Our approach: joint TDMA scheduling and nearly-optimal capacity allocation

• We call our approach a waterfilling-based TDMA scheduling

13

Waterfilling-based scheduling (1/2)

1 2 3 4t5 6t

T=10

1 2 3 4t5 6t

T=10

123 4

56

1 2 3 4t5 6t

T=10

123 4

56

1 2 3 4

5 6

2

3 5

4

1

6

1 2 3 4t5 6t

T=10

123 4

56

1 2 3 4

5 6

1 2 3 4

5 6

1 2 3 4t5 6t

T=10

123 4

56

1 2 3 4

5 6

1 2 3 4

5 6

12 3 4

56

14

Waterfilling-based scheduling (2/2)

15

Simulation Results

10 20 30 40 50 60 70 80 90 1000.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Throughpu vs. T

T

no

rma

lize

d c

ap

aci

ty

link1link2link3link4link5link6

16

Random Network, #links=30

50 100 150 200 250 300 350 400 450 500

0.08

0.09

0.1

0.11

0.12

0.13Throughput vs. T

T

Nor

mal

ized

Cap

acity

17

Conclusions

• We have studied the problem of optimal capacity allocation and scheduling in competitive wireless networks

• We proposed a mathematical model that captures the most relevant aspects of the capacity allocation problem: fairness, system optimality and uniqueness

• We developed a simple waterfilling algorithm that jointly solves the optimal capacity allocation and provides the corresponding collision-free TDMA scheduling

• Through simulations we have demonstrated the convergent properties of the proposed waterfilling algorithm

• Future work: find a distributed algorithm

18

Thank You!