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

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

3. LPF-F : Basic Idea Modify LPF to incorporate future information –Predict VOQ arrivals for next slot –Ľ ij = L ij + F ij where, L ij = current ocupancy of VOQ ij F ij = predicted future arrival in VOQ ij –Use Ľ ij to compute LPF

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

5. LPF-F : Prediction Technique Simple Adaptive AR Model:  (n) = [1- r(n)]  (n-1) + r(n) A(n-1) Where, A(n) = Arrival at n th time slot  (n) = Arrival Prediction for n th time 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. Q. How accurate should they be? Predictions will never be 100% accurate LPF-F : Inaccuracy In Predictions 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 as probabilities 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 n th time slot ij (n) = Estimated Arrival Rate at n th time slot for VOQ ij a = Arrival coefficient (1-a) reflects how much history is kept in ij s 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 L VOQold < L VOQnew, 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. RRS : Implementation Issues and Solutions 411 pointer at time n offset = d i didi OP port number of the arrival at input i, d i slots ago 0 M=2 k Input i d1d1 Input 1 dNdN Input N Geom(a) RV Generator Wrapped Geometric Distribution Pool of RVs N buffers, each buffer contains M cells M determines size of the history window A cell size of 1 byte allows N  256 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

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