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Memory Management Algorithms for DSM Switches

Memory Management Algorithms for DSM Switches. Huan Liu, Damon Mosk-Aoyama. Distributed Shared Memory Switch. What is known (for FIFO) 2N is necessary 3N-1 is sufficient Questions: Can we close the gap? Possible to have an implementable algorithm?. Our main results. On the gap

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Memory Management Algorithms for DSM Switches

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  1. Memory Management Algorithms for DSM Switches Huan Liu, Damon Mosk-Aoyama

  2. Distributed Shared Memory Switch • What is known (for FIFO) • 2N is necessary • 3N-1 is sufficient • Questions: • Can we close the gap? • Possible to have an implementable algorithm?

  3. Our main results • On the gap • Counter example to show 2.25N is necessary • A heuristic that uses 2.5N memories • On practical algorithms • Simulation results on simple algorithms under Bernoulli i.i.d. traffic

  4. 1 1 1 … 2 2 2 ? 3 3 ? 4 4 The counter example • Consider 4x4 switch • Can generalize to arbitrary N 5 5 Output 1 6 … 6 7 7 8 8 Output 4

  5. If we have N/4 more 1 1 1 6 6 Output 1 … 5 2 2 7 … 7 3 5 3 8 8 2 4 4 9 9 Output 4

  6. 1 1 1 1 2 2 2 2 3 3 3 3 7 6 5 4 Observation • Greedily minimizing the number of memories used can lead to trouble • Need to reuse memories later as time slot fills up 1 2 3 4

  7. 5 3 1 1 6 4 2 2 Heuristics with 2.5N memories • Minimize intersection between adjacent time slots • Minimize intersection between neighboring pairs • After N/2 cells arrived in a time slot, reuse memories already assigned to the adjacent time slot. • Simulation has been running for 100M+ cycles with no problem Minimize intersection 1 2 1 6 2 4 3 4

  8. Random algorithm • Assign memories to arriving cells randomly • Drop if another cell using the memory is • departing now • departing in the future in the same time slot Si …… S2 S1

  9. Upper bound on Drop Rate • Suppose there are memories. The drop probability is • The drop rate can now be computed as: • Use Si distribution from M/M/1

  10. Fixed Arrival Rate

  11. Fixed Number of Memories

  12. Distributed random algorithm • Each packet makes independent decision • Pick a random memory that is NOT • departing now • departing in the same time slot in the future • If two arriving packets pick the same memory, we drop one

  13. Distributed random algorithm - simulation

  14. Centralized random algorithm • Assign each packet in turn • Randomly pick a memory that is NOT • departing now • departing in the same time slot in the future • assigned for other packets arriving at the same time

  15. Centralized random algorithm - simulation

  16. Conclusion • Still gap  more work • Better counter example? • Prove 2.5N is sufficient • Also gap between theory and practical algorithm

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