1. Simulating Large Networks using Fluid Flow Model Yong Liu Joint work with Francesco LoPresti, Vishal Misra Don Towsley, Yu Gu

2. Outline Fluid Flow Model ODE solving Methods Account for Topology Computation Savings Model Adjustments Integration with Packet Level Simulators Open Issues

3. network TCP runs at the “edge” Routers within network drop/mark packets when buffers fill up Fluid Model of a Network of AQM Routers Supporting TCP Flows

4. TCP Congestion Control: window algorithm Window: can send W packets at a time increase window by one per RTT if no loss decrease window by half on detection of loss

5. TCP Congestion Control: window algorithm Window: can send W packets increase window by one per RTT if no loss decrease window by half on detection of loss sender receiver W

6. TCP Congestion Control: window algorithm Window: can send W packets increase window by one per RTT if no loss decrease window by half on detection of loss sender receiver W

7. Active Queue Management:RED RED: Random Early Detect proposed in 1993 Proactively mark/drop packets in a router queue probabilistically to –Prevent onset of congestion by reacting early –Remove synchronization between flows

8. The RED Mechanism RED: Marking/dropping based on average queue length x (t) (EWMA algorithm used for averaging) t min t max p max 1 2t max Marking probability p Average queue length x t -> - q (t) - x (t) x (t): smoothed, time averaged q (t)

9. Modeling RED: A Single Congested Router TCP flow i, prop. delay A i AQM router C, p One bottlenecked AQM router –service capacity {C (packets/sec) } –queue length q(t) – drop prob. p(t) N TCP flows –window sizes W i (t) –round trip time R i (t) = A i +q (t)/C –throughputs B i (t) = W i (t)/R i (t)

10. System of Differential Equations Window Size: All quantities are average values. Timeouts and slow start ignored Additive increase Loss arrival rate Mult. decrease Queue length: Outgoing traffic Incoming traffic

11. System of Differential Equations (cont.) Average queue length: Where  = averaging parameter of RED(w q )  = sampling interval ~ 1/C Loss probability: Where is obtained from the marking profile p x

12. Stepping back: Where are we? N+2 coupled equations solved numerically W=Window size, R = RTT, q = queue length, p = marking probability

13. Fluid Flow Model for a Network with Multiple Bottle-necks Scalable with link bandwidth and flow population within each class Network of M RED queues, K TCP classes, flows in class k

14. ODE Solving Methods Matlab ODE Solver Suit Error control, automatically adjusted step-size Cannot handle delayed differential equations Lack of flexibility of programming Computational Inefficiency Fixed Stepsize Runge-Kutta Method FFM: Time stepped numerical fluid model solver in C

15. Computation Cost: Matlab vs. FFM 80 TCP Classes x 20 RED Queues, Random Routing Matrix Matlab: 1572 seconds FFM: 5 seconds

16. Accuracy: FFM vs. NS Single Bottle Neck Network, 2 TCP Classes, Flows Per Class: 60  40  20

17. Account for Topology Fact: TCP sending rate will be reshaped in each queue it traverses C C Q1 Q2 Packet Loss Probability (I)Packet Loss Probability (II)

18. Account for Topology Keep track of each TCP class’s arrival rate and departure rate at each queue:

19. Account for Topology FFFM: Finer Fluid Flow Model Packet Loss Probability (I)Packet Loss Probability (II)

20. Refined Fluid Model Solver

21. Model Adjustment 1 In ns, actual packet drop/mark prob. is not equal to loss probability calculated from RED formula. Given a RED calculation value p, RED tries to make the interval between two drops/marks uniformly distributed in [1/p, 2/p] when “wait” option is on and [1, 1/p] when “wait” is off. Actual loss prob. is 2p/3 if “wait” on; 2p if “wait” off

22. Model Adjustment 1 With wait: Without wait:

23. Model Adjustment 2 NS won’t drop packet if the queue is empty Adjustment:

24. Other Adjustments TCP Newreno and SACK only backoff once for multiple losses within one window. Adjustment 1: Adjustment 2: At a given time, only TCP flows without packet loss will increase their congestion window.

25. {1,2}  {1}  {1,2,3} NS vs. FFFM

26. NS vs. FFFM (cont.) 3 TCP Classes, 8 RED Queues Scale bandwidth and flow population with k=1, 10, 50. Link Bandwidth: (black) 100M*k, (red) 10M*k Flows within each class: 40*k Class1 Class2 Class3

27. TCP Average Sending Rate, K=1 ClassNS Mean NS Std. FFF M Abs. Err. 142.01.7241.61.41 241.81.8441.21.54 317.21.4718.21.42 Class1Class2 Class3

28. Queue Length, K=1 QueueNS MeanNS Std.FFFMAbs. Err. 1100.418.799.114.5 279.626.174.620.2 Bottle-neck1 Bottle-neck2

29. TCP Average Sending Rate, K=10 ClassNS Mean NS Std. FFF M Abs. Err. 141.60.5941.60.47 241.40.6041.20.50 317.60.4718.20.64 Class1 Class2 Class3

30. Queue Length, K=10 QueueNS MeanNS Std.FFFMAbs. Err. 1995.459.5990.546.4 2779.2116.7745.796.0 Bottle-neck1Bottle-neck2

31. TCP Average Sending Rate, K=50 ClassNS Mean NS Std. FFF M Abs. Err. 142.50.2841.60.90 242.30.3141.21.09 316.70.2518.21.48 Class1Class2 Class3

32. Queue Length, K=50 QueueNS MeanNS Std.FFFMAbs. Err. 14875100495391.8 238492903729250 Bottle-neck1 Bottle-neck2

33. TCP Average Sending Rate, K=100 ClassNS Mean NS Std. FFF M Abs. Err. 141.80.2141.60.22 241.60.1941.20.38 317.40.1718.20.83 Class1Class2 Class3

34. Queue Length, K=100 QueueNS MeanNS Std.FFFMAbs. Err. 199421629905134 277902487457351 Bottle-neck1Bottle-neck2

35. Computation Savings

36. 0.00.1 1.0 1.1 1.3 1.2 1.4 1.5 4 2.02.1 2.22.3 0.2 Net 0 Net 1 Net 2 5 3.13.0 3.23.3 Net 3 Topology of a Large IP Network

37. Computation Cost

38. Integration with Packet Level Simulators Fluid flow model can provide delay and loss information for packets passing fluid network segments. If traffic from packet segments is negligible to fluid segment, fluid model can be solved independently. Simulated by FFFM Packet Level

39. Integration into NS FFFM has been integrated into NS by constructing Fluid Link and Fluid Network objects. Access Ns node Access Ns node Fluid Network Segment Fluid Network Topology of Hybrid NS Simulation Packet Network Segment

40. Hybrid NS Simulation Link Bandwidth: (black) 100M, (red) 15M 3 Background TCP Classes, 40 Flows per Class 3 Foreground TCP Sessions Class1 Session3 Session1 Class3 Class2 Session2 Fluid Network Segment Packet Level Nodes

41. Background TCP Average Window Size Class1 Class2Class3 hybrid packet

42. Foreground TCP Sample Path Session1 Session3 Session2

43. Bottle-neck Queue Evolution Bottle-neck1 Bottle-neck2 Simulation time: Hybrid: 8.4s, Packet: 29.7s CPU: 800MHz, Memory: 256M

44. Open Issues Time-out, Slow Start Finite duration flows, unresponsive flows High interaction between packet network segments and fluid network segments Limitations of mean value fluid model Verify results for large networks