Filipe Abrantes , João Taveira Araújo and Manuel Ricardo

1. 2008 Feb 27 Flash Crowd Effect in RCP Filipe Abrantes, João Taveira Araújo and Manuel Ricardo

2. Overview • Rate Control Protocol (RCP) • Modelling RCP with Flow Arrivals • Model Analysis • Validation through Simulation • Response to typical arrival distributions • Conclusion INESC Porto, 25-02-2008

3. Current Congestion Control (Context) • Embedded in TCP • Unstable • Inefficient • Increased delay • Limited fairness INESC Porto, 25-02-2008

4. Rate Control Protocol (RCP) • Explicit congestion control mechanism • New communication layer • (but can be embedded in TCP/IPv4 options, or IPv6 ext header) • Routers take an active role • High resolution explicit congestion information • Precise response (high util., near-zero delay) • Fast convergence time INESC Porto, 25-02-2008

5. Rate Control Protocol (RCP) • An RCP router computes a common rate R. • every flow bottlenecked at that router will use the rate R. • R is updated according to the spare bandwidth and the current outstanding queue • Instantaneous flow-fairness • No per-packet additions or multiplications required (unlike XCP) INESC Porto, 25-02-2008

6. Rate Control Protocol • Main Focus – Reducing Average Flow Completion Times (AFCT) • New flows jump-start to R (no slow start) • Reduces AFCT by 1 order to Reno, 2 orders to XCP • Each flow arrival causes temporary bandwidth overflow INESC Porto, 25-02-2008

7. Flash Crowds and RCP • We study the effect of Flash Crowds in RCP • Flash Crowd - significant and concentrated increase of the number of flows in the system. • When? • Events (Sports, Concerts, Political, ...) • Popular news sources (Slashdot, Digg, Del.icio.us, etc) • We should be able to characterise RCP behaviour in such cases • should assist system design. INESC Porto, 25-02-2008

8. RCP model • Simplifications • Abstract from packet granularity • Assume continuous control (rate adaptation is continuous) • Consider homogeneous delay (every flow has the same RTT) • Assume constant base delay (d0) • Nomenclature • y(t) represents input bandwidth • sum of the rate of all flows • d(t) represents system delay (RTT), for clarity we may only refer to it as d • d0 represents the base delay • q(t) represents queue length (persistent) • C represents bottleneck capacity INESC Porto, 25-02-2008

9. RCP model • Queue • Queue growth • Delay • Avg. Flow RTT • Input Bandwidth • Input BW Variation • RCP update equation Bandwidth Distributed each RTT(d) INESC Porto, 25-02-2008

10. Adding Dynamic Arrival of Flows • Growth rate (L) of the number of flows (N) each control interval • Revised dif. equation of input bandwidth • But d varies, L cannot be defined as constant growth • L itself affects d as we will see - recursive relation INESC Porto, 25-02-2008

11. Adding Dynamic Arrival of Flows • Growth rate (L) indexed to a fixed interval d_0 • Revised dif. equation of input bandwidth (Final) INESC Porto, 25-02-2008

12. What happens if the growth of traffic (flows) is constant? Queue builds to compensate the arrival of new flows Compensation Queue • Constant Growth Rate • Steady-State Conditions • Equilibrium property INESC Porto, 25-02-2008

13. RCP limits Stability limits for different β • Sustainable growth rate (L0) of flows is limited • Inversely proportional to β (approx) • β=0.226; Max Growth 6% each d0 (d0=base RTT) • 69% per second with RTT=100ms • β=0.4; Max Growth 12% each d0 • 312% per second with RTT=100ms INESC Porto, 25-02-2008

14. Model Validation • Start 5000 flows in periods of 5 to 20 seconds • Constant Growth L0 • d0=100 ms, C=1Gbit • Implemented on top of XCP present in ns-2 INESC Porto, 25-02-2008

15. Model Validation • Theory vs Sim (Steady-State) • Queue Length over Time (β=0.226) INESC Porto, 25-02-2008

16. How does L look like in typical distributions • We test 3 distributions • Laplace • Double exponential • Normal • Gaussian • Erlang Scheduled Events Spontaneous Events INESC Porto, 25-02-2008

17. How does L0 behave for typical arrival distributions - Laplace • b regulates the concentration of the arrivals INESC Porto, 25-02-2008

18. How does L0 behave for typical arrival distributions Higher peaks Laplace Normal Erlang INESC Porto, 25-02-2008

19. Distribution comparison • Laplace is the easier to control, Erlang the hardest • Steep increase rate of the number of flows, even if for a short period, easily unbalances the system severely • “Reasonable” (read below the stable limit) growth rate of the number of flows, even if persistent, is bearable • Conclusion • If we have the option to somehow shape the arrival of new calls try to follow a Laplace dist. (a form of slow start – exponential increase) INESC Porto, 25-02-2008

20. Possible counter measures • Embed some call admission mechanism in RCP to limit max L0 • A field in the RCP header could be used for that • Dynamically increase β • If queue average exceeds a certain threshold • If L0 exceeds the stable limit (if we can measure L0) INESC Porto, 25-02-2008

21. How does L0 translate to flash crowd size • RCP is able to absorb significant flash crowds β=0.226 β=0.4 INESC Porto, 25-02-2008

22. Study Limitations • Model Simplifications • Homogeneous rtt • Un-bounded queue • Negative queues not a problem • But upper bound should impact significantly • Convergence to steady-state (dynamic stability) • Not studied • Convergence will only occur for a region of values of α,β • Stable region is defined in other studies • Our simulations hint that the stable region is maintained in the presence of flash crowds INESC Porto, 25-02-2008

23. Conclusions • Presented an RCP model including the growth of the number of flows • Up to some growth limit, RCP “predicts” new flows by building up the queue • Able to accomodate significant flash crowds • Important that the flash crowd has a slow start • RCP deas best with Laplace dist., worse with Erlang-type dist. • The higher β is, the better RCP deals with the flash crowd (unsurprisingly) INESC Porto, 25-02-2008

24. Thank You Questions? INESC Porto, 25-02-2008

25. INESC Porto, 25-02-2008