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TDMA Scheduling in Competitive Wireless Networks
Mario Cagalj Hai Zhan
EPFL - I&C - LCA
February 9, 2005
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Presentation outline
• Introduction• System model and problem statement• Proposed solution - Waterfilling Algorithm• Simulation results• Conclusions
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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)
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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
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Example 1: network topology
link 1
collision domain 1
collision domain 2
link 3
link 2
link 5
link 6
link 4
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Example 1: link-based model
link 1
maximal clique 1
maximal clique 2
link 2link 3
link 5 link 6
link 4
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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
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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
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Waterfilling interpretation
• Simultaneously increase the rate of each link until some constraint(s) becomes binding
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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
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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
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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
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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
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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