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Using Traffic Models in Switch Scheduling

Using Traffic Models in Switch Scheduling. Hammad M. Saleem Imran Q. Sayed. June 3rd, 2002. LPF-Future (LPF-F). Rate Randomized Scheduler (RRS). Traffic Modeling. Two Categories. Make explicit predictions about future arrivals. Estimate current arrival rates

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Using Traffic Models in Switch Scheduling

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  1. Using Traffic Models in Switch Scheduling Hammad M. Saleem Imran Q. Sayed June 3rd, 2002

  2. LPF-Future (LPF-F) Rate Randomized Scheduler (RRS) Traffic Modeling Two Categories • Make explicit predictions about future arrivals • Estimate current arrival rates • (Make probabilistic predictions about future arrivals)

  3. LPF-F : Basic Idea • Modify LPF to incorporate future information • Predict VOQ arrivals for next slot • Ľij= Lij + Fij where, Lij = current ocupancy of VOQij Fij = predicted future arrival in VOQij • Use Ľij to compute LPF

  4. MWM - L LPF - Future Why LPF-F ?

  5. LPF-F : Prediction Technique • Simple Adaptive AR Model: • Â (n) = [1- r(n)] Â (n-1) + r(n) A(n-1) • Where, • A(n) = Arrival at nthtime slot • Â (n) = Arrival Prediction for nthtime slot (thresholded to give yes/no) • r (n) = Burstiness / Correlation between consecutive arrivals • r (n) = (1-a) * r(n-1) + a * A(n-1) XNOR A(n-2) • a reflects the adaptation of correlation coefficient

  6. LPF-F : Inaccuracy In Predictions • Predictions will never be 100% accurate Q. How accurate should they be? • Ans. At least 50%

  7. LPF-F : Results - 3x3 switch

  8. LPF-F : Results – 8x8 switch

  9. Rate Randomized Scheduler (RRS) :Basic Idea • Tassiulas Inspired Randomized Scheduling Algorithm • Keep an NxN matrix of current VOQ arrival rates • Random matching selection • Current VOQ arrival rates asprobabilities • Multiple iterations successively improve the weight of the match • Merge the new match with the one in memory • Add edges to unassigned ports in a Round Robin fashion

  10. RRS : Rate Matrix Calculation • Rate Equation - Weighted Moving Average • ij(n) = (1- a) ij(n-1) + a A(n-1) • Where, • A(n) = Arrival at nthtime slot • ij(n) = Estimated Arrival Rate at nthtime slot for VOQij • a = Arrival coefficient • (1-a) reflects how much history is kept in ijs • a reflects how much weight is given to recent arrivals

  11. RRS: Random Match Selection For each Iteration For each IP - Randomly select 0 or 1 OP based on corresponding VOQ arrival rates - If OP is unoccupied, Connect to it Else If LVOQold < LVOQnew, Disconnect OP from VOQold and Connect OP to VOQnew

  12. RRS : Results - I

  13. RRS : Results - II

  14. RRS : Results - III

  15. RRS : Results - IV

  16. RRS : Results - V

  17. d1 Input 1 Pool of RVs pointer at time n OP port number of the arrival at input i, di slots ago offset = di di Input i 4 11 Geom(a) RV Generator 0 M=2k Wrapped Geometric Distribution Input N dN • Pointer points to the same cell number in each buffer • Pointer writes a blank if there is no arrival in the slot • I RVs needed in each slot; I is the number of iterations • N buffers, each buffer contains M cells • M determines size of the history window • A cell size of 1 byte allows N  256 RRS : Implementation Issues and Solutions

  18. Stability Proofs • LPF-F • Predictions as bounded noise [A. Mekkittikul, N. McKeown] B = 2N • RRS • Probability of hitting MWM [L. Tassiulas]:   (amin)N

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