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On Providing Non-Uniform Scheduling Guarantees in a Wireless Network

On Providing Non-Uniform Scheduling Guarantees in a Wireless Network. Vartika Bhandari, Google Nitin H. Vaidya, University of Illinois. Network Model. Slotted time Single hop flows Time invariant link rates Goal: Network stability. Conflict Graph. Star conflict graph

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On Providing Non-Uniform Scheduling Guarantees in a Wireless Network

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  1. On Providing Non-Uniform Scheduling Guarantees in a Wireless Network Vartika Bhandari, Google Nitin H. Vaidya, University of Illinois

  2. Network Model • Slotted time • Single hop flows • Time invariant link rates • Goal: Network stability

  3. Conflict Graph • Star conflict graph • Maximal schedules link at the center, or, all other links Vertices represent links Edges  Conflicts

  4. Parameter Kl • Parameter Kl for link l = maximum # conflicting links that can be scheduled when l is not scheduled • Link at the center : 6 • Each remaining link : 1 • K = max over all links = 6

  5. Q P R S Throughput-Optimal Scheduler • Capacity region  possible to schedule traffic without causing unbounded queues • A throughput-optimal scheduler finds such a schedule  Stability region = Capacity region (u,v) RS Throughput PQ

  6. Q P R S Imperfect Scheduler Efficiency-ratio of imperfect scheduler = γ if: for load vector λ in stability-region, scheduler stabilizes load vector γλ RS PQ

  7. Q P R S Imperfect Scheduler Efficiency-ratio of imperfect scheduler = γ if: for load vector λ in stability-region, scheduler stabilizes load vector γλ RS PQ Does not capture situations such as this: RS PQ

  8. Relevance of Disparate per-Link Guarantees • Some links more critical than others • “differentiated QoS” • Average performance over all links may be more important than worst case link

  9. Q P R S Efficiency Vector Efficiency-Vector of = γif: For any load vector λin stability-region, the given scheduler stabilizes the network for load vector γλ(component-wise product ) RS γ= [0.5, 1] PQ γ= 0.5 Richer Characterization!

  10. Related Work • Sarkar, Chaporkar & Kar [WiOpt ’06]: • Per-link scaling (efficiency-vector) for maximal scheduling • Each link l’s scaling factor: xl =1/yl • Yl = max-over-links-m-in-I(l) (Km) • I(l) = set of links that interfere with l (includes l) • Kl = cardinality of maximal set of concurrently schedulable links in I(l) • Li & Negi • Uniform scaling results for maximal scheduler with priorities • Rate-stability

  11. Our Work • Studied how provable non-uniform scaling guarantees might be provided • Showed that introduction of prioritizationin existing maximal scheduling algorithms yields stronger non-uniform guarantees than without • All results for “queue-stability”

  12. Existing: Maximal Scheduler with Threshold Rule • Each link maintains a queue of packets to be sent • Threshold Rule • In each time-slot, a link competes for those channels c for which: ql ≥ rl • Maximal Schedule • computed amongst all competing (link, channel) pairs λ(t) Link l Channel d

  13. New:Local K-Precedence based Maximal Scheduler with Threshold Rule • Link l has priority K-Kl+1 • Threshold Rule • In each time-slot, a link competes for those channels c for which: ql ≥ rl • Prioritized Maximal Schedule • computed amongst all competing (link, channel) pairs • Either l in schedule or a higher/equal priority link in I(l) in schedule λ(t) Link l Channel d Result: each link l gets a scaling of 1/Kl

  14. A Generalization:General Prioritized Maximal Scheduler with Threshold Rule • Link l has priority pl • Multiple links may have same priority • Threshold Rule • In each time-slot, a link competes for those channels c for which: ql ≥ rl • Prioritized Maximal Schedule • computed amongst all competing (link, channel) pairs • Either l in schedule or a higher/equal priority link in I(l) in schedule λ(t) Link l Channel d

  15. Result for General Prioritized Scheduler • For a link l: • H(l)=set of links in I(l) with strictly higher priority than l • Z(l)= set of links in I(l) with equal priority to l • hl = max no. of concurrently schedulable links in H(l) U Z(l) • xl=max-over-links-m-in-(I(l)-H(l)) hm Result: link l can get arbitrarily close to a scaling of: 1/xl

  16. Existing:Centralized Greedy Maximal Scheduler • Centralized Greedy Maximal (CGM) Scheduler • Weight of a link: qlrl • In each time-slot: • Sort all valid links in non-increasing order of weight • Select link with largest weight; eliminate all links that conflict with this link • Repeat previous till no link left Known Uniform Scaling Result: 1/max(Kl)

  17. New:CGM Scheduler with Modified Weights • Weight of a link: qlrl/Kl Non-Uniform Scaling Result: link l gets scaling of 1/Kl

  18. Summary • Link priorities can help achieve desirable non-uniform guarantees Future Direction: A comprehensive study of how various protocol parameters can be modulated to achieve desired non-uniform guarantees.

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