1. Localized Asynchronous Packet Scheduling for Buffered Crossbar Switches Deng Pan and Yuanyuan Yang State University of New York Stony Brook

2. Outline Introduction Related work Localized asynchronous packet scheduling Simulation results Conclusions

3. Introduction Crossbar switches have long been the preferred structures for high speed switches and routers: Provide non-blocking capability. Overcome the bandwidth limitation of bus-based switches. Packet forwarding is simple.

4. Introduction For a crossbar switch, packets may be buffered at either Output ports Input ports Crosspoints

5. Introduction Output queued (OQ) switches only have buffer space at the output side. Achieve 100% throughput. Require speedup of N for an NxN switch. Input queued (IQ) switches only have buffer space at the input side. Require no speedup. Have to work with high time complexity algorithms in order to achieve 100% throughput.

6. Introduction Combined input-output queued (CIOQ) switches make a trade-off between the crossbar speedup and the complexity of the scheduling algorithms. Have small fixed speedup of two. Achieve 100% throughput with any iterative maximal matching algorithms. Emulate OQ switches.

7. Introduction Buffered crossbar switches are a special type of CIOQ switches. Each crosspoint of the crossbar has a small buffer. Crosspoint buffers eliminate the input and output contention. Buffered crossbar switches can directly schedule and switch variable length packets.

8. Introduction Previous scheduling algorithms for crossbar switches mainly focused on fixed length packet scheduling or cell scheduling. At input ports, new packets are segmented into fixed length cells. The cells are used as the scheduling units and transmitted across the switching fabric. At output ports, the cells are reassembled into original packets.

9. Introduction Variable length packet scheduling, or packet scheduling, improves the switch efficiency by avoiding the segmentation-and-reassemble (SAR) process. Higher throughput. Shorter packet latency. Lower hardware cost.

10. Introduction [Turner Infocom’06] proposed two packet scheduling algorithms for buffered crossbar switches. They can provide work-conserving guarantees, or emulate scheduling algorithms for OQ switches. They schedule packets by imposing an order on buffered packets. Each crosspoint needs 2L or more buffer space, where L is the maximum packet length.

11. Introduction We consider the other side of the problem, low time complexity and easy to implement packet scheduling algorithms. We present the Localized Asynchronous Packet Scheduling (LAPS) algorithm and analyze its performance. Local info based No comparison Crosspoint buffer size of L

12. Outline Introduction Related work Localized asynchronous packet scheduling Simulation results Conclusions

13. Related work Scheduling algorithms in the literature for buffered crossbar switches are generally designed with two possible objectives: To achieve high throughput. To emulate scheduling algorithms for OQ switches. The latter is a stronger requirement, but the implementation of the former can be simpler.

14. Related work Cell scheduling algorithms for high throughput CIXB-1, CIXOB-k, MCBF, SCBF… Cell scheduling algorithms to emulate scheduling algorithms for OQ switches GBVOQ_OCF, GBFG_SP, MCAF-LTF… Packet scheduling schemes Packet VOQ, Packet LOOFA, DPFQ…

15. Outline Introduction Related work Localized asynchronous packet scheduling Simulation results Conclusions

16. Localized asynchronous packet scheduling Structure of a buffered crossbar switch In i : input port Out j : output port B ij : crosspoint buffer Q ij : virtual queue The crossbar has speedup of two.

17. Localized asynchronous packet scheduling Based on the locations of the packets to be scheduled, there are three types of scheduling involved in a buffered crossbar switch. Input scheduling Crossbar scheduling Output scheduling

18. Localized asynchronous packet scheduling Output scheduling has been well studied, and various scheduling algorithms are proposed. Output scheduling usually does not affect the throughput performance as long as they are work-conserving. We use a simple FIFO algorithm for output scheduling, which is work-conserving.

19. Localized asynchronous packet scheduling For input scheduling, Select a backlogged virtual queue whose crosspoint buffer is empty, and send its head packet to the crosspoint buffer. When there are multiple eligible virtual queues, different arbitration rules can be used. Since the crossbar has speedup of two, the packet is sent to the crosspoint buffer with bandwidth 2R. Crossbar scheduling is similar.

20. Localized asynchronous packet scheduling In order to reduce the packet latency, cut- through switching can be used on the crossbar. Similarly, cut-through switching can be used at output ports.

21. Localized asynchronous packet scheduling

22. In input scheduling, the scheduling candidates of an input port are only the virtual queues whose crosspoint buffers are empty. This restriction simplify the implementation by enabling one bit to represent the status of the crosspoint buffer.

23. Localized asynchronous packet scheduling With speedup of two, LAPS achieves 100% throughput for any admissible traffic. Define Z ij (t)=Q ij (t)+B ij (t) If B ij is not empty at time t, ∑ k Z kj (t) has a negative derivative. If Q ij is not empty at time t, ∑ k Q ik (t) +∑ k Z kj (t) has a negative or zero derivative.

24. Localized asynchronous packet scheduling Assume that the traffic arrives according to a Poisson process and the packet length follows an exponential distribution with mean M. In i can be approximately modeled as an M/M/1 system, and accordingly

25. Localized asynchronous packet scheduling Hardware implementation Only local info is necessary, and it is suitable for distributed implementation and highly scalable. Since no comparison is necessary, the arbiters can implemented by priority encoders, which can make fast decisions in hardware. Since each crosspoint buffer needs only L buffer space, it minimize the cost for the switch.

26. Outline Introduction Related work Localized asynchronous packet scheduling Simulation results Conclusions

27. Simulation results We have conducted simulations to verify the 100% throughput of LAPS and to measure its delay and buffer requirement. We consider five different LAPS implementations: Fixed priority (FP) Random (RD) Round-robin (RR) Oldest packet first (OPF) Longest queue first (LQF)

28. Simulation results In order to reflect the burst nature of real network traffic, we emulate the incoming traffic by a Markov modulated Poisson process.

29. Simulation results We considered both uniform traffic and non- uniform traffic. The packet length in the simulation is uniformly distributed between [50, 1500] bytes. We consider a 16×16 switch, and each input port or output port has bandwidth of 1G bps.

30. Simulation results Throughput

31. Simulation results Average delay

32. Simulation results Maximum queue length

33. Outline Introduction Related work Localized asynchronous packet scheduling Simulation results Conclusions

34. Due to the introduction of crosspoint buffers, buffered crossbar switches can directly schedule and transmit variable length packets. Packet scheduling algorithms avoid SAR and are more efficient than cell scheduling algorithms. Higher throughput Shorter latency Lower hardware cost

35. Conclusions We presented the Localized Asynchronous Packet Scheduling (LAPS) scheme. Local info based No comparison Crosspoint buffer of size L We theoretically proved that LAPS achieves 100% throughput with speedup of two, and conducted simulations to verify the results.

36. Thank you! Questions?