Router Level Flow Control in Data Networks

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

2. Outline • 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

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

4. one hop controller Let Queue dynamics Link rate dynamics

5. one hop controller Router B Router A Router C

6. stability of one hop controller

7. Blocking C A E Congested router Slow link B D • 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 C A B D (queues in B are empty)

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

10. Back Pressure Forward Pressure Congested Router Data Control

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. A B C

13. A B C

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

15. Back Pressure constant input

16. Back Pressure input constant input input

17. Without Back Pressure

18. With Back Pressure

19. Forward Pressure Forward Pressure

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

21. Without forward pressure

22. With forward pressure

23. Blocking

24. Blocking

25. Blocking

26. 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 Minimize peak queue size Objective:

32. L1 Control methods subject to

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

38. Distributed Parameter Methods

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

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 4 2 3 Has a pole at zero, integrator

44. 1 4 Take the “sum” of possible input-output pairs. These sums lead to sensible 2 3 1 4 2 3

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