1 TDMA Scheduling in Competitive Wireless Networks Mario CagaljHai 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

6 Example 1: link-based model

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

9 Example 2: capacity allocation

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 finding 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)

14 Waterfilling-based scheduling (2/2)

15 Simulation Results

16 Random Network, #links=30

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!