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Low-complexity Scheduling for Wireless Networks

Low-complexity Scheduling for Wireless Networks. Guanhong Pei ∗ , V. S. Anil Kumar †. ∗ Dept. of ECE and Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA † Dept. of CS and Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA. ACM MobiHoc 2012.

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Low-complexity Scheduling for Wireless Networks

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  1. Low-complexity Scheduling for Wireless Networks Guanhong Pei∗, V. S. Anil Kumar† ∗ Dept. of ECE and Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA † Dept. of CS and Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA • ACM MobiHoc 2012

  2. Wireless Network Model • The network is modeled as a graph • Set of nodes: • Set of transmission links: • Wireless Interference • Graph-based interference model • Interference set for each link • and : interfering ⇔no successful tx at the same time • Interference relationship • Binary & Symmetric Data → receiver link sender ← ACK

  3. Physical Interference Model • SINR • Signal to Interference & Noise Ratio • Condition for successful transmission on link : Interference from to : interference : Signal attenuation rate Signal SINR at receiver of Background Noise Interference from all other transmitting links Threshold

  4. Traffic & Queueing Models • Traffic: Single-hop • Exogenous arrival processes: general i.i.d. • : # arrival packets to link at time ; • First moment: • Queueing: Each link is associated with a queue • : # packets queued on link l at time t • : # arrival packets on link l at time t • : # departure packets on link l at time t • : service rate offered to link l at time t Queue Arrival Departure Service Queue Evolution:

  5. Queueing Stability • Long-term average backlog: • Queue-stability of a system iff • In a stable system • long-term average arrival rate equalslong-term average throughput rate

  6. Throughput Region Graph Interference model Scheduling & Power Assignment scheme SP Max-Weight Scheduling Throughput region: ΛSPthe set of all stable traffic vectors under SP Capacity region: ΛOPTthe set of all stable traffic vectors γ-scaled region γΛOPT, (0 ≤γ≤1) γ: efficiency ratio (0≤γ≤1)

  7. The Problem • Distributed • Low-complexity • Scheduling & Power control • SINR Interference • Performance • Important Issues & Techniques Maximize the efficiency ratio

  8. Related Issues • Overhead of Control • Ambiguity in the Distributed Model • Questions • Outdated& infrequently-updatedcontrol info? • Performance impact? Trade-off?

  9. Summary of Results Low-complexity Distributed Scheduling & Power Control:Adaptive Random-access Algorithm Based on Queueing Info RA-SCHED : Interference Degreemax # independent links in any interference set Graph-based Interference: • Throughput • Region: Physical Interference: Link Diversity# classes of link lengths RA-SCHED-SINR Efficiency Ratio Single-hop Setting: • General stochastic traffic Infrequent info-exchange Use stale queueing info updated infrequently Random-access based on queue size info Negligible overhead No additional overhead for exchanging control information Techniques: • Power control policy: simple and flexible

  10. Efficiency Ratio of RA-SCHED-SINR • Link Diversity • Worst-case Efficiency Ratio in Practice • Can be Ω(1) • Link diversity is small in practice: • In the most extreme cases: kilometerscentimeters max. link length min. link length

  11. RA-SCHED Frame i-1 Frame i • Frame i+1 Frame: Info-exchange sub-frame Scheduling-txsub-frame Backlog info exchange Each link transmits with Prob. at time Channel-access Probability

  12. RA-SCHED: Details Each link transmits with Prob. at time Backlog info exchange • Variables: • : Backlog of at the start of frame • : Sum of of links in • : • Backlog info exchange: 2 rounds • (1) distribute to all the links in • (2) distribute to all the links in • Channel Access Prob. • if • For every time slot in the scheduling-tx sub-frame of Interference set of Frame: Info-exchange sub-frame Scheduling-txsub-frame

  13. Analysis of RA-SCHED Length: H1 Length: H2 prob. of a successful tx in an interference set: close to 1/e at each time t ofscheduling-tx sub-frame Frame: Efficiency Ratio: Info-exchange sub-frame Scheduling-txsub-frame If total average arrival in each interference set: The total queue size in the network w.h.p.in some period of time Necessary Condition of Stability For any H1, H2, such that The network is queue-stable Sufficient Condition of Stability

  14. Schedule Augmentation Preparation for RA-SCHED-SINR • Partition link set L into g(L) length classes {Li} • T-augmented schedule Slot under Policy S Super-slot under Policy T-augmented S 1 2 3 T-1 T

  15. RA-SCHED-SINR • A g(L)-augmented version of RA-SCHED • Channel-access Probability • Redefine Interference Set • Power Assignment • Links in the same length class use “similar” power • Including uniform, square-root, linear assignments • Backlog Info-exchange : a constant to be determined during analysis : a constant

  16. Analysis of RA-SCHED-SINR • Same workflow as RA-SCHED • However, “interference sets” are conceptual • Extra work: links maketransmission attempts bad good non-localnon-linear causeinterference deliverpackets upper-bound on interference lower-bound onprob. of successful transmission : a constant to be determined during analysis connected & balanced by parameter:

  17. Analysis of RA-SCHED-SINR (cont.) • Incorporate g(L) into efficiency ratio • in our SINR Setting Efficiency Ratio: Efficiency Ratio:

  18. Conclusion • Low-complexity Distributed Algorithms • Scheduling & power control • SINR interference, K-hop interference • Efficiency ratios: and • Outdated & Infrequently-updated control info • Future Work • Multi-hop traffic • Heterogeneous periods of control info update • Quantify delay throughput trade-off • Adaptive CSMA in SINR setting

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