1. Router Level Flow Control in Data Networks Stephan Bohacek University of Southern California

2. introduction 1-hop controllers –system description –stability –blocking 2-hop controllers –system description –classical design methods (intuition) hop over back pressure forward pressure time constant –modern design methods LQ L1 distributed parameter –stability future work and conclusions Outline

3. Objective: To avoid transmission of packets that will be dropped (best to drop packets at the entry point of the network). For very high speed networks it might be better to use hop-by-hop flow control instead of end- to-end flow control. Method: Control the router sending rates to ease and regulate network congestion. Problem: Sending a packet that will be dropped is inefficient.

4. Queue dynamics Link rate dynamics one hop controller Let

5. Router B one hop controller Router C Router A

6. stability of one hop controller

7. Blocking Slow link Congested router A B C D E The data leaving A is destined for C. The data leaving B is destined for D. Link E-D is slow, so the queue in E fills. Back pressure slows down both links A-E and B-E. However, the link from E-C is high speed, hence the link A-E is slowed needlessly.

8. two hop controller BA C D (queues in B are empty)

9. Queue Dynamics Rate Controller two hop controller How to set control parameters? intuition vs. optimization classical vs. modern

10. Congested Router Forward Pressure Data Control Back Pressure

11. As queue fills, out going data rates rapidly increase As queue fills, out going data rates slowly increase That is, the router sends data at the maximum rate whenever the queue is not empty.

12. ABC

13. ABC

14. Back Pressure AB C D If queue C-D fills Rate B-C slows Queue B-C fills Rate A-C slows Queue A-C fills

15. constant input Back Pressure

16. constant input input Back Pressure

17. Without Back Pressure

18. With Back Pressure

19. Forward Pressure

20. 1. input data 2. queue fills 3. data flows 4. queue fills 5. data flows rapidly - queue B-C is filling - queue A-C is filling ABC Forward Pressure

21. Without forward pressure

22. With forward pressure

23. Blocking

27. modern control methods (with truncation) optimal control with quadratic cost minimize peak queue/rate size distributed parameter

28. linear quadratic Quadratic Cost Let

29. Show plot of gains Note: gains decay, hence truncation LQ doesn’t make much use of back pressure lack of back pressure can be seen by the small gains from 26-27, 26-19 and 26-33

31. L1 Control methods Objective: Minimize peak queue size

32. subject to L1 Control methods

35. Note on previous slide, good back pressure, some forward pressure. But no back pressure from 8-5. Why? These optimization procedures don’t always give intuitive answers. Is it that the optimization procedure is better, or doing something stupid.

36. Distributed Parameter Methods Simple 1-D spatially invariant system I/O Data Flow Control Information

37. Temporal Dynamics (only depends on local variables) Spatial dynamics Distributed Parameter Methods

39. - Compact description of large system - Controllers will depend on local variables only Requires systems be homogeneous. Extending it to nonhomogeneous systems may lead to computational difficulties. advantages disadvantages - Distributed Parameter Methods

40. stability

42. Note that there still are some slow eigenvalues. These are from alphas that result in data taking a long time to get out of the network. That is, nonsensical alphas. It seems that making reasonable alphas is difficult The previous network is 3 x 3, with K4 and K6 = 0

43. 1 23 4 Has a pole at zero, integrator

44. 1 23 4 1 23 4 Take the “sum” of possible input-output pairs. These sums lead to sensible

46. stability

47. Future Directions characterization of alphas simulation with TCP and CBR data rigorous controller synthesis rigorous stability and performance analysis investigation of differences between TCP and CBR traffic in such a network