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Hashed and Hierarchical Timing Wheels

This paper by George Varghese and Tony Lauck explores various timer schemes like simple timer schemes, tree-based timers, timing wheels, and hashed timing wheels for efficient timer management in networks. The models and performance measures for different schemes are discussed.

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Hashed and Hierarchical Timing Wheels

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  1. Hashed and Hierarchical Timing Wheels A paper by George Varghese andTony Lauck

  2. Motivation • Timers are important for • Failure recovery, rate based flow control, scheduling algorithms, controlling packet lifetime in networks • Timer maintenance high if • Processor interrupted every clock tick • Fine granularity timers are used • # outstanding timers is high • Efficient timer algorithms are required to reduce the overall interrupt overhead

  3. Model & Performance Measure • Routines in the model • Client Invoked : • START_TIMER(Interval, Request_ID, Expiry_Action) • STOP_TIMER(Request_ID) • Timer tick invoked : • PER_TICK_BOOKKEEPING • EXPIRY_PROCESSING • Performance Measure • Space : Memory used by the data structures • Latency : Time required to begin and end any of the routines mentioned above

  4. Simple Timer Schemes (1 & 2) a b a b c c d d e e f Scheme 1: Can maintain absolute expiry time or the timer interval START_TIMER = O(1) STOP_TIMER = O(1) PER_TICK_BOOKKEEPING = O(n) Scheme 2: maintain absolute expiry time START_TIMER = O(n) STOP_TIMER = O(1) PER_TICK_BOOKKEEPING = O(1)

  5. Tree based timers (3) a a b b c c d d Can degenerate to a linear list in case of equal Interval timers START_TIMER = O(n) STOP_TIMER = O(1) PER_TICK_BOOKKEEPING = O(1) Scheme 3: maintain absolute expiry time START_TIMER = O(log(n)) STOP_TIMER = O(1) PER_TICK_BOOKKEEPING = O(1)

  6. Scheme 4 Keep a large timing wheel A cursor in the timing wheel moves one location every time unit (just like a seconds hand in the clock) If the timer interval is within a rotation from the current curser position then put the timer in the corresponding location Simple Timing Wheel (4) 0 1 7 2 6 3 5 4 START_TIMER = O(1) STOP_TIMER = O(1) PER_TICK_BOOKKEEPING = O(1)

  7. Say wheel has 8 ticks Timer value = 17 Make 2 rounds of wheel + 1 more tick Schedule the timer in the bucket “1” Keep the # rounds with the timer At the expiry processing if the # rounds > 0 then reinsert the timer Hashed Timing Wheel (5+6) # of rounds remaining 2 4 0 1 7 2 6 3 1 2 5 4 2 1 1 2

  8. Hashed Timing Wheel • Scheme 5: Sorted Lists in each bucket • The list in each bucket can be insertion sorted • Hence START_TIMER takes O(n) time in the worst case • If n < WheelSize then average O(1) • Scheme 6: Unsorted list in each bucket • List can be kept unsorted to avoid worst case O(n) latency for START_TIMER • However worst case PER_TICK_BOOKKEEPING = O(n) • Again, if n < WheelSize then average O(1)

  9. 3 3 1 7 5 3 5 1 Hierarchical Timing Wheel 0 1 7 2 6 3 4 5 3 5 0 1 7 Hours wheel 2 6 3 7 5 4 0 5 1 7 2 1 1 2 6 3 Minutes wheel 4 5 Seconds wheel

  10. Hierarchical Timing Wheels • Scheme 6, extension 2 • START_TIMER = O(m) where m is the number of wheels • The bucket value on each wheel needs to be calculated • STOP_TIMER = O(1) • PER_TICK_BOOKKEEPING = O(1) on avg.

  11. Comparison *Overflow list

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