New Designs for the Internet Why can’t I get higher throughput? Why is my online video jerky? How is capacity shared in the Internet?

Some Internet History 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 “A Brief History of the Internet”, the Internet Society

TCP 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; } time [0-8 sec] bandwidth [0-100 kB/sec]

How TCP shares capacity sum of flow bandwidths time available bandwidth individual flow bandwidths

Random Walks, Electrical Networks Kakutani (1945) Consider a particle performing a random walk on a network

Random Walks, Electrical Networks Kakutani (1945) Consider a particle performing a random walk on a network From node i it jumps to neighbouring node j at rate 1/r ij i j r ij

Random Walks, Electrical Networks Kakutani (1945) Consider a particle performing a random walk on a network From node i it jumps to neighbouring node j at rate 1/r ij

Random Walks, Electrical Networks Kakutani (1945) Consider a particle performing a random walk on a network From node i it jumps to neighbouring node j at rate 1/r ij

Random Walks, Electrical Networks Kakutani (1945) Consider a particle performing a random walk on a network From node i it jumps to neighbouring node j at rate 1/r ij

Random Walks, Electrical Networks Kakutani (1945) Consider a particle performing a random walk on a network From node i it jumps to neighbouring node j at rate 1/r ij

Random Walks, Electrical Networks Kakutani (1945) Consider a particle performing a random walk on a network From node i it jumps to neighbouring node j at rate 1/r ij

Random Walks, Electrical Networks Let V i be the probability that, starting at i, the particle hits node 1 before it hits node 0 Let I ij =(V j -V i )/r ij node 1 node 0 ViVi

Random Walks, Electrical Networks Let V i be the probability that, starting at i, the particle hits node 1 before it hits node 0 Let I ij =(V j -V i )/r ij Then V i are the potentials and I ij the currents in this electrical circuit node 1 node 0 resistance r ij

Three Levels of Description Microscopic: particle-level rules of motion Macroscopic: Ohm’s law and Kirchhoff’s laws Teleological: I ij are such as to minimize heat dissipation minimize ½  i,j I ij 2 r ij over I ij

Macroscopic description Consider several TCP flows sharing a single link Let RTT be the round-trip time [sec] Let x be the mean bandwidth of a flow [pkts/sec] Let y be the total bandwidth of all flows [pkts/sec] Let C be the total available capacity [pkts/sec] The total fraction of packets that are lost is p = (y-C) + /y The TCP algorithm achieves average increase in rate = average decrease in rate 1/RTT 2 = (p x) x/2

Teleological description Consider several TCP flows sharing a single link Let RTT be the round-trip time [sec] Let x r be the mean bandwidth of flow r [pkts/sec] Let y be the total bandwidth of all flows [pkts/sec] Let C be the total available capacity [pkts/sec] TCP and the network act so as to solve maximise  r U(x r ) - (y - C log y/C-1) + over x r where y=  r x r x U(x)U(x)

Teleological description Consider several TCP flows sharing a single link Let RTT be the round-trip time [sec] Let x r be the mean bandwidth of flow r [pkts/sec] Let y be the total bandwidth of all flows [pkts/sec] Let C be the total available capacity [pkts/sec] TCP and the network act so as to solve maximise  r U(x r ) - (y - C log y/C-1) + over x r where y=  r x r x U(x)U(x) little extra valued attached to high- bandwidth flows severe penalty for allocating too little bandwidth

Teleological description Consider several TCP flows sharing a single link Let RTT be the round-trip time [sec] Let x r be the mean bandwidth of flow r [pkts/sec] Let y be the total bandwidth of all flows [pkts/sec] Let C be the total available capacity [pkts/sec] TCP and the network act so as to solve maximise  r U(x r ) - (y - C log y/C-1) + over x r where y=  r x r x U(x)U(x) small RTT large RTT

Teleological description Consider several TCP flows sharing a single link Let RTT be the round-trip time [sec] Let x r be the mean bandwidth of flow r [pkts/sec] Let y be the total bandwidth of all flows [pkts/sec] Let C be the total available capacity [pkts/sec] TCP and the network act so as to solve maximise  r U(x r ) - (y - C log y/C-1) + over x r where y=  r x r x U(x)U(x) no penalty until y>C i.e. the link is overloaded

Teleological description Is this what we want the Internet to optimize? Does it make good use of the network? Can it deliver high bandwidth? Is it a fair allocation? Can we design a better allocation? x U(x)U(x)

Stability of TCP TCP was designed to prevent congestion collapse. How well does it work? A more detailed macroscopic model for TCP is Is this dynamical system stable? How fast does it converge?

Ongoing work Kelly (Cambridge statslab) Vinnicombe (Cambridge engineering) proposed+analysed a good macro model Tom Kelly (CERN) implemented it in Linux: ScalableTCP Raina (Cambridge management science) analysed stability & instability Wischik (UCL computer science) micro/macro models for the link: how big should buffers be?

Ongoing work Low, Doyle (Caltech electrical engineering) Proposed further micro/macro models, FAST TCP Cottrell (SLAC) Testbed for TCP variants Srikant (UIUC electrical/computer engineering) Towsley (UMass computer science) Fluid model analysis Baccelli (ENS mathematics) Marsan (Turin electrical engineering) Mean field limit theory for TCP