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Internet congestion control

Internet congestion control. Damon Wischik, UCL. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A. What is queueing theory for?. Given the arrival process, what is

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Internet congestion control

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  1. Internet congestion control Damon Wischik, UCL TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAA

  2. What is queueing theory for? DJW 2006 2/24 • Given the arrival process, what is • We often seek limit theorems to describe the arrival process, and to approximate this probability • Typical motivation: “this lets us choose buffer size etc. to ensure that queue overflow is rare” • This does not make sense for Internet queues, since TCP (which governs most Internet traffic) deliberately causes the queue to overflow arrival process queue Example: for a queue with N independent flows, each self-similar with Hurst parameter H, then for some,  >0

  3. Some Internet history DJW 2006 3/24 • 1974: First draft of TCP/IP[“A protocol for packet network interconnection”, Vint Cerf and Robert Kahn] • 1983: ARPANET switches on TCP/IP • 1986: Congestion collapse • 1988: Congestion control for TCP[“Congestion avoidance and control”, Van Jacobson]

  4. TCP transmission control protocol DJW 2006 4/24 • Internet congestion is controlled by the end-systems • The TCP algorithm, running on the server, decides how fast to send data • It sends data packets, and waits for ACKnowledgement packets • It sets a target window size wtthe number of packets that have been sent but not yet acknowledged (here 5+3) • The average transmission rate is xt≈wt/RTT where RTTis the round trip time • It adapts wt based on the ACKs it receives acknowledgements Server (TCP) User data

  5. TCP DJW 2006 5/24 if (seqno > _last_acked) { if (!_in_fast_recovery) { _last_acked = seqno; _dupacks = 0; inflate_window(); send_packets(now); _last_sent_time = now; return; } if (seqno < _recover) { uint32_t new_data = seqno - _last_acked; _last_acked = seqno; if (new_data < _cwnd) _cwnd -= new_data; else _cwnd=0; _cwnd += _mss; retransmit_packet(now); send_packets(now); return; } uint32_t flightsize = _highest_sent - seqno; _cwnd = min(_ssthresh, flightsize + _mss); _last_acked = seqno; _dupacks = 0; _in_fast_recovery = false; send_packets(now); return; } if (_in_fast_recovery) { _cwnd += _mss; send_packets(now); return; } _dupacks++; if (_dupacks!=3) { send_packets(now); return; } _ssthresh = max(_cwnd/2, (uint32_t)(2 * _mss)); retransmit_packet(now); _cwnd = _ssthresh + 3 * _mss; _in_fast_recovery = true; _recover = _highest_sent; } transmission rate [0–100 kB/sec] time [0–8 sec]

  6. How TCP shares capacity DJW 2006 6/24 individual flow rates available capacity aggregate flow rate time

  7. How to describe a network DJW 2006 7/24 Some networks admit models at three different levels: • Microscopic rules of behaviour for the individual elements • e.g. rules of motion of electrons • Macroscopic laws that describe the behaviour of aggregates • e.g. Kirchhoff’s law, Ohm’s law • Teleological principles that describe the operating point to which the system settles down • e.g. Thomson’s principle

  8. TCP model I: the sawtooth DJW 2006 8/24 • Consider a single link, and a single flow with round trip time RTT • When the link is not congested, transmission rate xt increases by 1/RTT i2 pkt/sec every sec • When the link becomes congested, transmission rate is cut by 50% service capacity transmissionrate x(t) * * * buffer size queuesize time queue becomes full and packets are dropped TCP realizes there is congestion, and cuts its rate

  9. TCP model II: billiards DJW 2006 9/24 • Consider a single link, and many flows with round trip times RTT(1), RTT(2),... • When the link is not saturated, flow r increases its transmission rate xt(r) by 1/RTT(r) pkt/sec2 • When the link becomes saturated, some flows experience packet drops and they cut their rates • Assume some probabilistic model that says which flows experience drops [Baccelli+Hong 2002] + + = * * * * * * *

  10. TCP model III: fluid DJW 2006 10/24 • Individual TCP flows follow a sawtooth + + individual flow rates + + = = aggregate flow rate time

  11. TCP model III: fluid DJW 2006 11/24 • Individual TCP flows follow a sawtooth • ... but many TCP flows added together are smoother • the average rate xt varies according to a time-delayed differential equation • eqn involves pt, the packet drop probability experienced by packets sent at time t [Misra+Gong+Towsley 2000, Baccelli+McDonald+Reynier 2002, after Kelly et al. 1998] + + individual flow rates + + = = aggregate flow rate time

  12. TCP model III: fluid DJW 2006 12/24 • There are three possible limit models for describing the behaviour of the queue and calculating the drop probability • TCP selects a limiting model, depending on the size of the buffer Round trip time RTT N TCP flows Service rate NC Buffer size B(N)

  13. Three buffer-sizing regimes DJW 2006 13/24 • These three regimes are qualitatively different; they are described by different dynamical systems, operating over different timescales • The relationship between buffer size and timescales was first observed by [Deb+Srikant, 2004] small buffers B(N)=B medium buffers B(N)=B√N • large buffers • B(N)=BN dropprobability[0–.3] queuesize[0–B pkt] trafficintensity[0–1] time [0–5s] queue size[(B-25)–B pkt] time [50ms]

  14. Instability / synchronization DJW 2006 14/24 • Sometimes the dynamical system for the network is unstable, and the queue size flip-flops • This means there are short periods of concentrated packet loss • This might manifest itself as a burst of static in an Internet telephone call • In fact, this corresponds to the billiards model for TCP • Engineers can use the dynamical system description of TCP to help them design the network so that it is stable queuesize[0–619pkt] TCPwindowsizes[0-25pkt] time [0–5s]

  15. Equilibrium analysis DJW 2006 15/24 • A well-designed network should be stable, i.e. it should reach some equilibrium state • How can we characterize the equilibrium state?

  16. Teleological description U(x) x DJW 2006 16/24 • The equilibrium state is the solution to the optimization problem Round trip time RTT N TCP flows;flow r has rate xr Service rate C Mediumbuffer size

  17. Teleological description DJW 2006 17/24 • The equilibrium state is the solution to the optimization problem Round trip time RTT N TCP flows;flow r has rate xr Service rate C Buffer sizemedium little extra value attached to high-throughput flows U(x) x severe penalty for allocating too little throughput

  18. Teleological description DJW 2006 18/24 • The equilibrium state is the solution to the optimization problem Round trip time RTT N TCP flows;flow r has rate xr Service rate C Buffer sizemedium flows with large RTT are satisfied with just a little throughput U(x) x flows with small RTT demand higher throughput

  19. Teleological description DJW 2006 19/24 • The equilibrium state is the solution to the optimization problem Round trip time RTT N TCP flows;flow r has rate xr Service rate C We should thus set up caches very close to the user, even if that means putting them in a congested part of the network Buffer sizemedium flows with large RTT are satisfied with just a little throughput U(x) x flows with small RTT demand higher throughput

  20. Teleological description U(x) x DJW 2006 20/24 • The equilibrium state is the solution to the optimization problem Round trip time RTT N TCP flows;flow r has rate xr Service rate C Buffer sizemedium there is no penalty until the link is overloaded, i.e. y>C The network seeks to be overloaded, leading to poor quality for Internet telephone calls

  21. Maths conclusion DJW 2006 21/24 • TCP chooses its own limit regime • TCP, through its adaptive feedback mechanism, induces a fluid limit over the timescale of a round trip time • The queue dynamics change fluidly over the timescale of a round trip time, and stochastically over much shorter timescales • The choice of buffer size determines which of three queueing models is relevant

  22. Design conclusion DJW 2006 22/24 • The TCP code admits description at two higher levels • a dynamical system model at the macroscopic level • a welfare optimization problem at the teleological level • This gives us insight into how to extend TCP • make sure the dynamical system is stable • choose a more desirable optimization problem • These insights have led to new ideas about routing, load balancing, choice of buffer size in core routers, quality of service, high-speed TCP

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