Compiled from work by: Lachlan Andrew (2), Steven Low (1),

1. Comparison of MaxNet and XCP: Network Congestion Control using explicit signallingSpeaker: Bartek Wydrowski Compiled from work by: Lachlan Andrew (2), Steven Low (1), Iven Mareels (2), Bartek Wydrowski (1), Moshe Zukerman (2). (2) (1)

2. Talk Overview • MaxNet & XCP Overview. • Steady state: Rate allocation properties. • Summary of Maxnet and XCP. • Maxnet: A little more details • Stability. • Convergence Speed.

3. Network Congestion Control L1 S1 D1 L2 S2 D2 L3 S3 D3 Sources transmit at a rate controlled by a “congestion signal” Links generate the congestion signal based on level of congestion at link Congestion level of end-to-end path is fed back to source

4. Network Congestion Control Congestion signal on the Internet is implicit, and can be modelled as the sum of the end-to-end link congestion levels – this is where XCP, MaxNet differs. S p p p i 1 2 N Link 1 Link 2 Link N Source Destination Link l drops packets at rate pl: Link l ECN marks packets at rate pl: Link l delays packets for time pl: Link 1 Link 2 Link 1 Link 2 Link 1 Link 2 T1 T2

5. MaxNet: Overview

6. MaxNet: Quick Overview • MaxNet is: • A Fully distributed flow control architecture for large networks. • Max-Min fair in principle. • Stable for networks of arbitrary topology, number of users, capacity and delay. • Fast convergence properties. • Addresses short-flow control. • Philosophy: • Simple Architecture. • Ability to scale. • Simplicity  ability to design/predict.

7. MaxNet: Packet Format Packet Data CongestionSignal N Bits (price_k)

8. MaxNet: Source Algorithm x– Transmission Rate p - Price Source Algorithm – Demand Function. Each source can have a different demand function which determines the source’s relative need for capacity. Xi = D(price_k) Congestion Feedback from ACK k Source rate Source demand function

9. MaxNet: Packet Marking Source 1 Packet Signal = max(PacketSignal,p1(t)) Source 2 Packet Signal = max(PacketSignal ,p2(t)) Packet Signal = max(PacketSignal ,p3(t)) Signal =max(p2,p3) Signal =max(p1,p2,p3)

10. MaxNet: Link Algorithm Router Algorithm: Packet marking according to Price_k = max ( Price_k , pl(t) ) Link price updated at each control interval, say every 10ms. (single price for all flows on link) Congestion signal in pkt k pl(t+1) = pl(t) + b(y(t)-aC) Constant: convergence speed Link capacity Aggregate input rate Constant to control Link utilization

11. MaxNet: Steady State Properties S0 2 Mbps D0 L1 3 Mbps S1 D1 L2 2 Mbps S2 D2 L3 S3 D3 q0 = p1 = max(p1) q1 = p1 = max(p1,p2) q2 =p1= max(p1,p2,p3) q3 = p3= max(p2, p3) p1 p2 p3 Mbps S3 1.33 S0,S1,S2 0.66 q3 q0, q1, q2 Price

12. MaxNet: Steady State Properties Link 2 capacity Link 2 capacity 3 Mbps 3 Mbps 1 Mbps 1 Mbps T1 T2 T1 T2

13. XCP: Overview

14. XCP Architecture XCP Packet Header H_cwnd H_rtt H_feedback Receiver Sender router router 1. Initializes pkt k: H_throughput_k H_rtt_k H_feedback_k 2. Each Router Computes Feedback: H_feedback_k = min(H_feedback_k,H_lk) Where H_lk = link l’s feedback for pkt k. Thus, feedback from router with minimum ‘feedback signal’ is obtained from source to destination path. 3. Send header back to sender in ACK.

15. XCP Architecture Source Algorithm: • Rate is governed by window • Source sends packet containing XCP header • Source receives feedback in ACK and adjusts window Feedback from ACK Change in source window Source transmission rate

16. XCP Architecture Router Algorithm: Feedback computed for each packet H_feedback_k = min (H_feedback_k,H_feedback_i) Round trip time of source i in packet Feedback in Pkt k header Window of source i in packet Mean of all RTTs Packet size Sum over control interval Aggregate input rate Link capacity Queue

17. MaxNet, XCP: Steady State Properties

18. MaxNet: Steady State Properties MaxNet is Max-Min fair for homogenous sources. If all sources have the same demand function (homogenous),then MaxNet results in a max-min rate allocation.Max-min fairness maximises the minimum rate allocation,and maximizes each subsequently larger rate without reducingthe smaller rates.

19. MaxNet: Steady State Properties For general demand functions, MaxNet is weighted min-max fair. (Min-Max price fair) Sources can prioritizetheir rate allocation bychanging their demandfunctions. Roughly speaking,their rate allocation will be in proportion to the magnitude of the demand function. Transmission rate x1 x2 Link price

20. XCP: Steady State Properties • Analysis to compute XCP equilibrium rates for arbitrary topology: Steven H. Low, Lachlan L. H. Andrew, Bartek P. Wydrowski, “Understanding XCP: Equilibrium and Fairness”. Rate allocation is a solution to a max-min problem with additional constraints • Effects of additional constraint: • Utilization can be below 100%. • Rates can be arbitrarily small fraction of max-min fair rates • In some topologies, residual terms are redundant.

21. XCP: Steady State Properties • Given a topology, our analysis can predict rate allocation. • Matches NS2 results very precisely • Predicts interesting pathological cases

22. XCP: Steady State Properties • Utilization of a link varies with number of sources bottlenecked at other links. • Lower and upper bound are: • ρl = fraction of flows at link l not bottlenecked at link l • l= fraction of traffic at link l not bottlenecked at link l •  = shuffling parameter  ,  = XCP parameters (conv speed,buffer) • With standard alpha and gamma parameters, utilization is at least 80%.

23. XCP Scenario 1 C1=155 Mbps C2=200 Mbps Alpha = 0.4 Beta = 0.226 Gamma = 0.1

24. XCP Utilisation

25. XCP Scenario 1 Rate allocation can be arbitrarily smaller than max-minfair rates. Eg: C1=155 Mbps C2=C1(n-1)/n i=n^2-1 j=1 Alpha = 0.4 Beta = 0.226 Gamma = 0.1

26. XCP Max-Min Fairness

27. XCP- Stability counter-example Sources 0..9 Sink Source 10 200Mbps 1x = 50ms 5x = 250ms 10x = 500ms 100Mbps 50ms

29. MaxNet & XCP comparison

30. XCP & MaxNet Research status

31. MaxNet: Stability Properties

32. MaxNet Stability MaxNet is stable (local proven) over arbitrary network dimensions of: Number of sources, links,hops, delay, capacity Same properties as were shown for SumNet in: F. Paganini, J.C. Doyle and S.H. Low, “Scalable laws for stable network congestion control,” in Proc. IEEE Conf. Decision Contr. (CDC), (Orlando, FL), 2001, pp. 185-90.

33. Network Control Model L1 S1 D1 L2 S2 D2 L3 S3 D3 Physical Network Control Model Network Model quantities are small signal variations about equilibrium. S1 Source Rate x Aggregate price q S2 S3 0 0 0 0 L1 0 L2 0 0 L3 0 Aggregate Rate y Link price d

34. Network Control Model MaxNet open-loop transfer function. S1 S2 S3 0 0 0 0 L1 0 L2 0 0 L3 0 Source Gain Link Gain Link Integrator Action Backward Routing Matrix Forward Routing Matrix

35. MaxNet Stability Requirements x– Transmission Rate p - Price Source Gain Constrains slope Of source demand function Link Gain Constrains speedof link control law pl(t+1) = pl(t) + b(y(t)-aC)

36. MaxNet: Convergence Properties

37. MaxNet: Convergence Speed MaxNet has faster asymptotic convergence than the SumNet architecture. (MaxNet is able to place the dominant pole further to the left than SumNet.)

38. SumNet, MaxNet simulations

39. Conclusion • MaxNet steady state, stability and speed properties have been investigated. • XCP steady state properties were recently analyzed. • MaxNet offers (at least) steady state and implementation simplicity, advantages over XCP.