Distributed Low-Complexity Maximum Throughput Scheduling in Wireless Backhaul Networks Abdul Kader Kabbani (Stanford University) Theodoros Salonidis (Thomson) Edward Knightly (Rice University)

Wireless Backhaul Networks (WBN) Key features Multi-hop wireless networks Tree logical structures Applications WiFi mesh networks (802.11s) Mobile Multihop Relay (MMR) 802.16j

WBN scheduling constraints Primary interference Constraints due to single-radio limitation Links with common node endpoints cannot transmit simultaneously Secondary interference Links with distinct node endpoints Endpoints should not be within range Two kinds of systems Multi-channel: only primary interference Single-channel: both primary and secondary interference a b X c d e g f h

WBN scheduling constraints Primary interference Constraints due to single-radio limitation Links with common node endpoints cannot transmit simultaneously Secondary interference Links with distinct node endpoints Endpoints should not be within range Two kinds of systems Multi-channel: only primary interference Single-channel: both primary and secondary interference a b X c d e g f h

Scheduled Access MAC in WBNs Operation Slot-Synchronization Fixed-size multi-slot frames Frame = Scheduling Phase + Data phase S D … Frame i-1 Frame i Frame i+1 Data phase: a set of conflict-free links must transmit Scheduling phase: decides the link set of data phase

Major challenges Scheduling policy at Data phase Scheduling phase Which conflict-free links should be scheduled to transmit at each frame? Scheduling phase How can the nodes decide the conflict-free set using a simple and distributed protocol?

Maximum throughput scheduling Performance Guarantees All feasible rates (max-throughput) Scheduling policy in Data Phase MWIS policy: Select a set of conflict-free links with maximum sum of queue backlogs [Tassiulas92] a 2 4 5 3 1 b c d e g f h

Maximum throughput scheduling Performance Guarantees All feasible rates (max-throughput) Scheduling policy in Data Phase MWIS policy: Select a set of conflict-free links with maximum sum of queue backlogs [Tassiulas92] a 2 4 5 3 1 b c d e g f Scheduling phase No efficient centralized or distributed protocol exists to date No bound on scheduling phase duration h

Maximal scheduling Scheduling policy in Data Phase Select a maximal conflict-free link set Performance guarantees Single-channel: >1/8 of feasible rates Multi-channel: >1/2 of feasible rates [Shroff05, Srikant06, Sarkar06] a 2 4 5 3 1 b c d e g f h

Maximal scheduling Scheduling policy in Data Phase Select a maximal conflict-free link set Performance guarantees Single-channel: > 1/8 of feasible rates Multi-channel: > 1/2 of feasible rates [Shroff05, Srikant06, Sarkar06] a 2 4 5 3 1 b c d e g f h Scheduling phase Single-channel: 2N steps, distributed protocol Multi-channel: unknown

Our contributions For any WBN network WBN-MWIS distributed protocol Maximum throughput scheduling can be realized in at most 2(N-1) steps in scheduling phase Duration of scheduling phase can be further reduced to O(logN) steps (constant per frame). WBN-MWIS distributed protocol For both single-channel and multi-channel systems

WBN topology properties Conflict Graph (CG) Edge xy = link x and link y interfere a 2 4 5 3 1 Single-channel CG a b c d e g h f b c d e g f h

WBN topology properties Conflict Graph (CG) Edge xy = link x and link y interfere a 2 4 5 3 1 a b c d e g h f Multi-channel CG b c d d e g f h h WBN CG recursive property At least one vertex v forms a clique with all its neighbors. When v is removed, resulting subgraph has same property

WBN-MWIS protocol Offline computation Online computation Weight phase Pre-compute a sequence links will be visited during each scheduling phase. a 2 4 5 3 1 b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase Visit each link according to the pre-computed sequence and subtract its weight from weight of all interferers h d e f g a b c c b a g f e d h h

WBN-MWIS protocol Offline computation Online computation Weight phase Pre-compute a sequence links will be visited during each scheduling phase. a 2 4 5 3 1 b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase Visit each link according to the pre-computed sequence and subtract its weight from weight of all interferers h d e f g a b c c b a g f e d h h

WBN-MWIS protocol Offline computation Online computation Weight phase Pre-compute a sequence links will be visited during each scheduling phase. a 2 1 5 -1 b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase Visit each link according to the pre-computed sequence and subtract its weight from weight of all interferers h d e f g a b c c b a g f e d h h

WBN-MWIS protocol Offline computation Online computation Weight phase Pre-compute a sequence links will be visited during each scheduling phase. a 2 1 4 -1 b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase Visit each link according to the pre-computed sequence and subtract its weight from weight of all interferers h d e f g a b c c b a g f e d h h

WBN-MWIS protocol Offline computation Online computation Weight phase Pre-compute a sequence links will be visited during each scheduling phase. a -1 2 b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase Visit each link according to the pre-computed sequence and subtract its weight from weight of all interferers h d e f g a b c c b a g f e d h h

WBN-MWIS protocol Offline computation Online computation Pre-compute a sequence links will be visited during each scheduling phase. a -1 2 b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase: TRAV link set constructed h d e f g a b c c b a g f e d h h MWIS phase Construct a maximal link set by visiting the links of TRAV set in reverse sequence order

WBN-MWIS protocol Offline computation Online computation Pre-compute a sequence links will be visited during each scheduling phase. a b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase: TRAV link set constructed h d e f g a b c c b a g f e d h h MWIS phase Construct a maximal link set by visiting the links of TRAV set in reverse sequence order

WBN-MWIS protocol Offline computation Online computation Pre-compute a sequence links will be visited during each scheduling phase. a b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase: TRAV link set constructed h d e f g a b c c b a g f e d h h MWIS phase Construct a maximal link set by visiting the links of TRAV set in reverse sequence order

WBN-MWIS protocol Offline computation Online computation Pre-compute a sequence links will be visited during each scheduling phase. a 2 4 5 3 1 b c d e g f 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 E.g. Online computation Weight phase: TRAV link set constructed h d e f g a b c c b a g f e d h h MWIS phase Construct a maximal link set by visiting the links of TRAV set in reverse sequence order

WBN-MWIS protocol overhead Overhead = scheduling phase duration Minimize number of slots in scheduling phase Exploit spatial reuse for both Weight-phase and MWIS phase. For regular tree topologies O(logN) (constant per frame).

WBN-MWIS protocol overhead Example: D=2, L=5 (N=63) Per-frame overhead typically less than 10% Lower overhead for multi-channel systems

WBN-MWIS vs. Maximal Protocol (Single-channel) Relative throughput performance Maximal provides 1/8 rates of WBN-MWIS Overhead ratio r=BWN-MWIS/Maximal for D-ary trees of depth L (single-channel systems) 0.02% < r < 75% E.g. D=2, L=5, WBN-MWIS has 50% overhead of Maximal Exponential decrease on L Polynomial decrease on D

Conclusions WBN-MWIS: a distributed maximum throughput scheduling protocol of low complexity. Offline: enumeration procedure Online: weight phase + MWIS phase Overhead Does not depend on weights O(N) in worst case and O(logN) after offline optimizations. Low in practice, both in absolute terms and relative to protocols realizing suboptimal policies.