Enabling Distributed Throughput Maximization in Wireless Mesh Networks - A Partitioning Approach

1. Enabling Distributed Throughput Maximization in Wireless Mesh Networks - A Partitioning Approach Andrew Brzezinski, Gil Zussman, and Eytan Modiano Laboratory for Information and Decision Systems Massachusetts Institute of Technology, Mobicom06 Speaker : Janghwan Lee

2. Overview • This paper studies the throughput optimization in a wireless mesh network (WMN) where • multiple orthogonal channels are available; • each host has multiple radios; • distributed transmission scheduling is used. • Two control knobs: • Channel assignment (network partition) • Transmission scheduling algorithm

3. Overview Set of SA Set of CA + = ca(i) sa(j) Level 1 Global capacity • For a multi-channel wireless network, we can • Try all possible (channel assignment, scheduling algorithm) pairs, and use the pair that gives best performance. • Given the channel assignment, try all scheduling algorithms and use the one that gives best performance. • Given the channel assignment, use the distributed scheduling algorithm [J.-H. Hoepman]. Set of SA + = ca sa(j) Level 2 Local capacity + = ca dsa Level 3 Achievable

4. Overview • Usually for the performance obtained from previous three schemes, we have • Special topology: In some network topologies [Dimakis and Walrand], we have • Special CA: CA that partition the network into subnetworks of special topologies. Level 1 Level 2 Level 3 Level 2 Level 3 Set of CA + + Subset of special CA ca(i) dsa ca(i) osa

5. Overview • Outline: • Study of topologies in which simple distributed maximal scheduling algorithms can achieve 100% throughput (identifying the special subset). • Channel allocation algorithms • which channel assignment in the subset is best? • Assumption • Primary interference constraints • Multi-radio and multi-channel WMNs

6. e12 2 Model 4 5 e24 e45 e13 1 3 e23 Interference Graph • Network Graph • Traffic: the packet arrivals at every link are mutually independent and temporally i.i.d. processes with arrival rate and the column vector is • Link Activation: is a column vector (with ) representing a possible link activation of the network. • Stability Region (Λ*) : the set of all admissible arrival rate vectors.

7. Study of Topologies • OLoP [A. Dimakis and J. walrand]: if satisfy OLoP, then is a special topology. • Forests are special topologies A tree satisfies LoP A clique satisfies LoP Primary interference constraint If is a tree, then is a clique of tree A tree of cliques satisfies LoP Trees are special topologies If G1 and G2 are special then G1 U G2 is special Forests are special topologies

8. Channel Allocation Set of CA Subset of special CA Forest CA • Guideline: partition the network into k forests. • Strategy: • Channel assignment (Network Partitioning): • Stage 1: Forests formation using either Breadth-First Search (BFS) or Matroid Cardinality Intersection (MCI). • Stage 2: Three algorithms to adjust this partition to get another special partition which has larger network capacity. • Scheduling Algorithm: distributed approximation algorithm [J.-H.Hoepman] with (local) computational complexity O(1). new k forests Stage 1 BSF or MCI k forests Stage 2 Adjustment Scheduling (dsa) Original Topology

9. Capacity Expansion • Which partition is better? • Given a rate vector (0.5,0.5,0.5,0.5,1), it is admissible in partition 1 but not admissible in partition 2. • Partition 1 has larger capacity. Original topology Partition 1 Partition 2

10. Capacity Expansion A B D • Smaller node degree implies larger capacity. • Unfortunately, either MCI or BFS algorithm doesn’t assign links uniformly among channels. • Adjustment: balance the number of edges across channels and reduce the node degrees in each channel. C A A A B D B D B D C C C A A A B D B D B D C C C

11. Capacity Expansion • Three algorithms • R-GREEDY: Minimize the maximum degree by directly reassign channel of the target link. • Maximum degree reallocation algorithm (R-MAXD): Minimize the maximum degree by re-running MCI. • Average degree reallocation algorithm (R-AVGD): reduce any vertex degree in the graph as long as the reduction • does not lead to degree increase on vertices with higher degree • does not lead to more vertices of maximum degree elsewhere in the graph.

12. Performance Evaluation • Original partition (MCI) • R-GREEDY • R-MAXD • R-AVGD

13. Performance Evaluation • Performance metrics for random networks with different number of nodes • Average Capacity: the average packets per timeslot per edge over all edges the network. • Worst Case Capacity: the lowest capacity allocated to a link in the network.

14. Comments • Pros: • A rigorous study of the set of topologies which are special ones. • A novel approach to eliminate the gap between performance of optimal scheduling and distributed scheduling.

15. Comments • Cons: • The authors use primary interference constraint, which is unrealistic. Therefore their scheduling is overoptimisitc. R1 S1 S2 R2

16. Comments • Does graph theoretical approach is suitable for WMN problem? • Separation of channel assignment and adjustment(balancing) • Any other better solution? – lack of comparison

17. Questions?