1. Reduced Rate Switching in Optical Routers using Prediction Ritesh K. Madan, Yang Jiao EE384Y Course Project

2. Outline Motivation for reduced rate switching A generalized architecture in optical switching Delay analysis for the architecture Motivate the choice of architecture and prediction Prediction using Least Mean Square Algorithm Convergence of prediction algorithm and stability Effectiveness of prediction through simulation results

3. Reduced Rate Switching Architectures Why? Using a optical switching element could use less power, simplify architecture But it takes a while to reconfigure (~  sec)

4. Reduced Rate Switching Architectures A switching element takes multiple time slots to change between configurations. During the transition, the switch can not transfer packets. time Decision Time MWM schedule based on current VOQ sizes Switch transfer packets based the schedule

5. Reduced Rate Switching Architectures A switching element takes multiple time slots to change between configurations. During the transition, the switch can not transfer packets. Multiple switches can be time multiplexed, so that for any time slot, one of switches can transfer packets. time Decision Time

6. A switching element takes multiple time slots to change between configurations. During the transition, the switch can not transfer packets. Multiple switches can be time multiplexed, so that for any time slot, one of switches can transfer packets. Or, keep a switching element in a configuration for more than one time slot, time Decision Time Burst Length Reduced Rate Switching Architectures

7. A switching element takes multiple time slots to change between configurations. During the transition, the switch can not transfer packets. Multiple switches can be time multiplexed, so that for any time slot, one of switches can transfer packets. Or, keep a switching element in a configuration for more than one time slot, so a less number of switches can be used. time Decision Time Burst Length Reduced Rate Switching Architectures

8. Architecture Choice Decision time = m Burst Length = k Number of switches needed = m/k+1 time Decision Time Burst Length Example m=8, k=4, need 3 switches: tt+mt+m+k How many switches should we use?

9. Effect of Burst Length Rapidly diminishing benefit of increasing the number of switches

10. Effect of Burst Length Rapidly diminishing benefit of increasing the number of switches Speedup does not help much Where is the delay coming from?

11. Where is the delay from? Bound on average delay can be obtained: –by method proposed by Devavrat et. al. 02. –Or by the drift analysis method proposed by Leonardi et. al. 01. For uniform i.i.d. traffic, the bound is:  is the load at a input, N is the number of inputs Does the average queue size really have a linear dependency on m + k ? time Decision Time Burst Length tt+mt+m+k

12. Key observation Decision time = m and Burst length = k has the accumulative effect of increasing the delay by ~ m + k : Decision time: VOQ’s that should be served m time slots ago are served now. Burst length: Effect of arrivals from t-k to t will not show up until time t. time Decision Time Burst Length tt+mt+m+kt-k arrivals

13. Key observation Decision time = m and Burst length = k has the accumulative effect of increasing the delay by ~ m + k How do we reduce the delay caused by the decision time and burst length, while using only 2 switches? time Decision Time Burst Length tt+mt+m+kt-k arrivals

14. Key observation Decision time = m and Burst length = k has the accumulative effect of increasing the delay by ~ m + k How do we reduce the delay caused by the decision time and burst length, while using only 2 switches? –Prediction! –Intuition: at time = t, correctly guessing the VOQ sizes at t + m eliminates the delay caused by the Decision Time time Decision Time Burst Length tt+mt+m+kt-k arrivals

15. Effect of prediction Prediction reduces the wait time for the queue that should be served.

16. To decide schedule for burst (n+1) –observe VOQ at beginning of burst n (decision instant) –predict arrivals during burst n –know departures during burst n –do MWM on time Decision Time Burst Length Scheduling Scheme burst nburst (n+1)

17. Adaptive Linear Prediction w i [n] are the weights at beginning of burst n are the arrivals to a single VOQ during burst n weights are adapted with time

18. Prediction Scheme z -1 Adaptive linear combiner with (L+1) weights Adaptive Linear Combiner with (L+1) weights + a[n] a[n-1] e[n] a pred [n+1] error signal for adaptation copy weights a[n] a pred [n]

19. Adaptation of weights using LMS … Error e[n] a[n-1] z -1 … a[n-L-1]a[n-2] a pred [n] (predicted value) a[n] (true value) w 0 [n-1] w 1 [n-1] w L [n-1]

20. Convergence of LMS For second order stationary arrivals, Convergence is guaranteed if Rate of convergence

21. Stability of Scheduling Algorithm Theorem 1: Under Bernoulli i.i.d. arrivals, MWM on predicted queue lengths gives 100% throughput for any decision time and burst length Proof: Decision time + burst length = m + k < infinity => Number of arrivals in m + k time slots is finite => For stationary arrivals the weight vector converges => Error in guessing the queue length is bounded => W MWM - W pred < C => 100% throughput

22. Simulation (6X6 Switch) with  =1333, a=0.5decision time = burst length =64