Queueing theory for TCP

Queueing theory for TCP PowerPoint PPT Presentation


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DJW 2007 2/24. . 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 _1141

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Queueing theory for TCP

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1. Queueing theory for TCP Damon Wischik, UCL Gaurav Raina, Cambridge

2. DJW 2007 2/24 Multiplicative decrease -- when network is congested, load grows exponentially (transmit, retransmit, reretransmit...) Additive increase -- helps with fairness (of relatively greater benefit to low-bandwidth users) Devised by Jain+Ramakrishnan (1988) DECbitMultiplicative decrease -- when network is congested, load grows exponentially (transmit, retransmit, reretransmit...) Additive increase -- helps with fairness (of relatively greater benefit to low-bandwidth users) Devised by Jain+Ramakrishnan (1988) DECbit

3. DJW 2007 3/24 Models for TCP

4. DJW 2007 4/24 Models for TCP

5. DJW 2007 5/24 Models for TCP

6. DJW 2007 6/24 Models for TCP

7. DJW 2007 7/24 Simulation results

8. DJW 2007 8/24 Simulation results

9. DJW 2007 9/24 Formulate a maths question What is the limiting queue-length process, as N??, in the three regimes large buffers B(N)=BN intermediate buffers B(N)=BvN small buffers B(N)=B Why are these the interesting limiting regimes? What are the alternatives? [Bain, 2003] Interest in these limits? WANT: increasing capacity. Current TCP either has moderate or small rates; to understand current TCP need N flows. (To understand future TCP: consider TCP algorithm parameterized by N.) Buffers: these are the three regimes people are interested in.Interest in these limits? WANT: increasing capacity. Current TCP either has moderate or small rates; to understand current TCP need N flows. (To understand future TCP: consider TCP algorithm parameterized by N.) Buffers: these are the three regimes people are interested in.

10. DJW 2007 10/24 Intermediate buffers B(N)=BvN Consider a standalone queue fed by N Poisson flows, each of rate x pkts/sec where x varies slowly, served at constant rate NC, with buffer size BvN i.e. an MNx//DNC //1/BvN queue xt=0.95 then 1.05 pkts/sec, C=1 pkt/sec, B=3 pkt Observe queue size fluctuates very rapidly; busy periods have duration O(1/N) so packet drop probability pt is a function of instantaneous arrival rate xt queue size flips quickly from near-empty to near-full, in time O(1/vN) packet drop probability is pt=(xt-C)+/xt

11. DJW 2007 11/24 Intermediate buffers B(N)=BvN Consider a standalone queue fed by N Poisson flows, each of rate x pkts/sec where x varies slowly, served at constant rate NC, with buffer size BvN i.e. an MNx//DNC //1/BvN queue xt=0.95 then 1.05 pkts/sec, C=1 pkt/sec, B=3 pkt Observe queue size fluctuates very rapidly; busy periods have duration O(1/N) so packet drop probability pt is a function of instantaneous arrival rate xt queue size flips quickly from near-empty to near-full, in time O(1/vN) packet drop probability is pt=(xt-C)+/xt

12. DJW 2007 12/24 Closing the loop In the open-loop queue we assumed Poisson inputs with slowly varying arrival rate queue size flips quickly from near-empty to near-full queue size fluctuates very rapidly, with busy periods of duration O(1/N), so drop probability pt is a function of instantaneous arrival rate xt In the closed-loop TCP system the round trip time means that we can treat inputs over time [t,t+RTT] as an exogenous arrival process to the queue the average arrival rate should vary slowly, according to a differential equation the aggregate of many point processes converges to a Poisson process, and this carries through to queue size [Cao+Ramanan 2002]

13. DJW 2007 13/24 Intermediate buffers B(N)=BvN 2Gb/s link, C=50 pkt/sec/flow 5000 TCP flows RTT 150–200ms buffer 619pkt simulator htsim by Mark Handley, UCL

14. DJW 2007 14/24 Intermediate buffers B(N)=BvN 2Gb/s link, C=50 pkt/sec/flow 5000 TCP flows RTT 150–200ms buffer 619pkt simulator htsim by Mark Handley, UCL

15. DJW 2007 15/24 Instability and synchronization When the queue is not full, there is no packet loss, so transmission rates increase additively When the queue becomes full, there are short periods of concentrated packet loss This makes the flows become synchronized

16. DJW 2007 16/24 Large buffers B(N)=BN

17. DJW 2007 17/24 Small buffers B(N)=B

18. DJW 2007 18/24 Conclusion

19. DJW 2007 19/24 Conclusion

20. DJW 2007 20/24 Instability & buffer size On the basis of these models, and of a control-theoretic analysis of the limit cycles that ensue, we claimed a buffer of 30–50 packets should be sufficient intermediate buffers will make the system become synchronized, and utilization will suffer large buffers get high utilization, but cause synchronization and delay

21. DJW 2007 21/24 Instability & buffer size On the basis of these models, and of a control-theoretic analysis of the limit cycles that ensue, we claimed a buffer of 30–50 packets should be sufficient intermediate buffers will make the system become synchronized, and utilization will suffer large buffers get high utilization, but cause synchronization and delay

22. DJW 2007 22/24 Burstiness The problem is that the Poisson limit breaks down A key step in the C+R proof is showing that each flow contributes at most one packet in a busy period But TCP, on a fast access link, will produce bursty traffic: sources can send an entire window-full of packets back-to-back For very fast access speeds, i.e. very bursty TCP traffic, a batch-M/D/1/B model is appropriate

23. DJW 2007 23/24 Burstiness & access speeds Simulations of a system with a single bottleneck link with capacity NC, where each flow is throttled by a slow access link

24. DJW 2007 24/24 Burstiness & access speeds Simulations of a system with a single bottleneck link with capacity NC, where each flow is throttled by a slow access link

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