1. 1 Analysis of a window-based flow control mechanism based on TCP Vegas in heterogeneous network environment Hiroyuki Ohsaki Cybermedia Center, Osaka University, Japan oosaki@cmc.osaka-u.ac.jp

2. 2 Contents  Introduction  Analytic model Window-based flow control based on TCP Vegas Window-based flow control based on TCP Vegas Heterogeneous network Heterogeneous network  Analysis of throughput and fairness  Analysis of stability and transient behavior  Numerical examples Two bottleneck links with 30 TCP connections Two bottleneck links with 30 TCP connections  Conclusion

3. 3 TCP (Transmission Control Protocol)  Packet retransmission mechanism Retransmit lost packets in the network Retransmit lost packets in the network  Congestion avoidance mechanism A window-based flow control mechanism A window-based flow control mechanism  Several versions of TCP TCP Tahoe TCP Tahoe TCP Reno TCP Reno TCP Vegas TCP Vegas

4. 4 TCP Vegas  Advantages over TCP Reno A new retransmission mechanism A new retransmission mechanism An improved congestion avoidance mechanism An improved congestion avoidance mechanism A modified slow-start mechanism A modified slow-start mechanism  Uses measured RTT as feedback information 1. Measures RTT for a specific packet 2. Estimates severity of congestion 3. Changes window size  Packet loss can be prevented

5. 5 Objectives  Analyze a window-based flow control Congestion avoidance mechanism of TCP Vegas Congestion avoidance mechanism of TCP Vegas Connections with different propagation delays Connections with different propagation delays Several bottleneck links Several bottleneck links Using a control theoretic approach Using a control theoretic approach  Show numerical examples Throughput and fairness Throughput and fairness Stability and transient behavior Stability and transient behavior

6. 6  Source host maintains the minimum RTT:   Source host measures the actual RTT: r(k)  Window size is changed based on d(k) Congestion avoidance of TCP Vegas

7. 7 Assumptions  Network topology is arbitrary  All routers employ static routing  All routers have a FIFO buffer for each port  All TCP connections are symmetry  Backward path is never congested

8. 8  Window size of connection c : w c  c : control parameter that determines the amount of increase/decrease in window size State transition equation: window size

9. 9 State transition equation: queue length  Queue length of the buffer for link l : q l b(c,l) : the previous link of link l for connection c b(c,l) : the previous link of link l for connection c l c : the access link of connection c l c : the access link of connection c

10. 10 Throughput and fairness  Focus on equilibrium values (denoted by *)  c * : throughput of connection c  c * : throughput of connection c  c * : sum of all queuing delays of connection c  c * : sum of all queuing delays of connection c  Can be regarded as a Little's law  Fairness between TCP connections c and c'

11. 11 Stability and transient behavior  Obtain a linearized model x(t) : state vector (current state – equilibrium state) x(t) : state vector (current state – equilibrium state)  LCM : Lowest Common Multiple of all  c /  's  LCM : Lowest Common Multiple of all  c /  's  Eigenvalues of A determine stability and transient behavior

12. 12 Numerical example: network model  Two bottleneck links and 30 TCP connections C1 C2 N2 C3 Source Host Destination Host Router N1 N3 L1L2

13. 13 Numerical example: throughput  Effect of difference in link capacities (  l1 = 20) 0 1 2 3 4 5 6 7 8 9 10 020406080100 Throughput (packet/ms) Link capacity of l2 (packet/ms)  c1 *  c2 *  c3 *

14. 14 Numerical example: stability  Effect of link capacity (  l = l1 = l2) 0 1 2 3 4 5 6 7 01234567  l = 0.2  l = 2  l = 20  l = 200  l = 2000 Control parameter  c of connection C1 Control parameter  c of connection C2, C3

15. 15 Conclusion  Analytic model Window-based flow control based on TCP Vegas Window-based flow control based on TCP Vegas Homogeneous network Homogeneous network  Throughput and fairness Can be explained by Little's law Can be explained by Little's law Has a bias against link capacity and # of bottleneck links Has a bias against link capacity and # of bottleneck links Window size in steady state Window size in steady state  (bandwidth) x (propagation delay) + (control parameter  c )

16. 16 Conclusion (cont.)  Stability and transient behavior Determined by eigenvalues of state transition matrix A Determined by eigenvalues of state transition matrix A Link capacity significantly affects stability Link capacity significantly affects stability Investigation using trajectories of eigenvalues Investigation using trajectories of eigenvalues  Future work More simulation studies More simulation studies Extension to TCP Tahoe or TCP Reno Extension to TCP Tahoe or TCP Reno