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

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

4. Network Congestion Control Source Destination Link 2 Link N Link 1 S i p 2 p 1 p N 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. Link l drops packets at rate p l : Link l ECN marks packets at rate p l : Link l delays packets for time p l : Link 1 Link 2 Link 1 Link 2 Link 1 Link 2 T1T1 T2T2

5. MaxNet: Overview

6. 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. MaxNet: Quick Overview

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

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

9. Packet Signal = max(Packet Signal,p 1 (t)) Packet Signal = max(Packet Signal,p 2 (t)) Packet Signal = max(Packet Signal,p 3 (t)) Signal =max(p 1,p 2,p 3 ) Source 1 Signal =max(p 2,p 3 ) Source 2 MaxNet: Packet Marking

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

11. MaxNet: Steady State Properties S2 S1 S0 L1 L2 L3 D1 D0 D3S3 D2 2 Mbps 3 Mbps 2 Mbps q 0, q 1, q 2 0.66 1.33 q3q3 S3 S0,S1,S2 Mbps Price p1p1 p2p2 p3p3 q 3 = p 3 = max(p 2, p 3 ) q 0 = p 1 = max(p 1 ) q 1 = p 1 = max(p 1,p 2 ) q 2 = p 1 = max(p 1,p 2,p 3 )

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

13. XCP: Overview

14. XCP Architecture H_cwnd H_rtt H_feedback XCP Packet Header Sender Receiver 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: Change in source window Source transmission rate Feedback from ACK Rate is governed by window Source sends packet containing XCP header Source receives feedback in ACK and adjusts window

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

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 reducing the smaller rates.

19. For general demand functions, MaxNet is weighted min-max fair. (Min-Max price fair) MaxNet: Steady State Properties x1x2x1x2 Link price Transmission rate Sources can prioritize their rate allocation by changing their demand functions. Roughly speaking, their rate allocation will be in proportion to the magnitude of the demand function.

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

26. XCP Max-Min Fairness

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

29. MaxNet & XCP comparison CriteriaMaxNetXCP Rate AllocationMaxMin Weighted MaxMin Constrained MaxMin (less than MaxMin) Bits per Packet Naïve encoding: 40 Bits/pkt with naïve linear encoding. Smarter encoding: 4 Bits/pkt (effectively) Every n th packet carries signal, say n=10, and exponential encoding of price. 96 Bits/pkt from BSD implementation. Router operations per packet 2 = 1 addition +1 max 12 = 3 multiplications + 1 division + 6 additions + 2 comparisons

30. XCP & MaxNet Research status CriteriaMaxNetXCP StabilityLinear stability for networks of arbitrary size, RTTs, capacity and number of flows proven. Linear stability for single link and aggregate of flows, all with same RTT. Have counter example for more general case. Convergence Speed Linear analysis shows faster convergence than ECN, loss (RENO), delay (FAST,VEGAS) based schemes. No control analysis available. Some simulation results show faster than TCP- RENO. Implementation progress Custom Simulation, TCP-FAST can be adopted. NS2 BSD

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 S2 S1 S3 L1 L2 L3 D2 D1 D3 S1 S2 S3 L2 L3 L1 0 00 0 00 0 0 Physical Network Control Model Network Source Rate x Aggregate price q Link price d Aggregate Rate y Model quantities are small signal variations about equilibrium.

34. Network Control Model Forward Routing Matrix Backward Routing Matrix Source GainLink Gain Link Integrator Action MaxNet open-loop transfer function. S1 S2 S3 L2 L3 L1 0 00 0 00 0 0

35. Source Gain Link Gain MaxNet Stability Requirements p - Price x– Transmission Rate Constrains slope Of source demand function Constrains speed of link control law p l (t+1) = p l (t) +  (y(t)-  C)

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.