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1 Colored GSPN Models for the QoS Design of Internet Subnets Marco Ajmone Marsan IEIIT-CNR and Politecnico di Torino - Italy Eindhoven – June 27, 2003 ICATPN 2003

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2 The first law of invited talks Disappointment is proportional to the speaker’s fame

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3 Venice 1988 My previous invited talk at ICATPN Goal: convince researchers to use GSPN models

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4 Today Original goal: publish a paper that I thought nobody would accept … …but the paper was accepted!

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5 Today New goal: explain why (IMO) GSPN models (and discrete- state models in general) are becoming inadequate for Internet modeling

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6 Colored GSPN Models for the QoS Design of Internet Subnets ? Marco Ajmone Marsan IEIIT-CNR and Politecnico di Torino - Italy Eindhoven – June 27, 2003

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7 Outline The Internet today Dimensioning IP networks GSPN and Queuing network models Fluid approaches Conclusions

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8 Outline The Internet today Dimensioning IP networks GSPN and Queuing network models Fluid approaches Conclusions

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9 Source: Internet Software Consortium (http://www.isc.org/)

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10 Source: Internet Traffic Report (http://www.internettrafficreport.com/)

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11 Source: Internet Traffic Report (http://www.internettrafficreport.com/)

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12 Source: Internet Traffic Report (http://www.internettrafficreport.com/)

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13 Source: Internet Traffic Report (http://www.internettrafficreport.com/)

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14 Source: Sprint ATL (http://ipmon.sprint.com/packstat)http://ipmon.sprint.com/packstat April 7th 2003, 2.5 Gbps link

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15 Source: Sprint ATL (http://ipmon.sprint.com/packstat)http://ipmon.sprint.com/packstat April 7th 2003, 2.5 Gbps link

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16 Source: Sprint ATL (http://ipmon.sprint.com/packstat)http://ipmon.sprint.com/packstat April 7th 2003, 2.5 Gbps link

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17 Source: Sprint ATL (http://ipmon.sprint.com/packstat)http://ipmon.sprint.com/packstat April 7th 2003, 2.5 Gbps link

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18 Source: Sprint ATL (http://ipmon.sprint.com/packstat)http://ipmon.sprint.com/packstat April 7th 2003, 2.5 Gbps link

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19 Source: Sprint ATL (http://ipmon.sprint.com/packstat)http://ipmon.sprint.com/packstat April 7th 2003, 2.5 Gbps link

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20 Source: Sprint ATL (http://ipmon.sprint.com/packstat)http://ipmon.sprint.com/packstat April 7th 2003, 2.5 Gbps link

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21 Source: Sprint ATL (http://ipmon.sprint.com/packstat)http://ipmon.sprint.com/packstat April 7th 2003, 2.5 Gbps link

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22 And still growing... Subject: [news] Internet still growing 70 to 150 per cent per year Date: Mon, 23 Jun 2003 09:55:45 -0400 (EDT) From: CAnet-NEWS@canarie.ca... Andrew Odlyzko, director of the Digital Technology Center at the University of Minnesota,... says Internet traffic is steadily growing about 70 percent to 150 percent per year. On a conference call yesterday to discuss the results, he said traffic growth slowed moderately over the last couple of years, but it had mostly remained constant for the past five years....

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23 Outline The Internet today Dimensioning IP networks GSPN and Queuing network models Fluid approaches Conclusions

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24 Over 90 % of all Internet traffic is due to TCP connections TCP drives both the network behavior and the performance perceived by end-users Analytical models of TCP are a must for IP network design and planning Consideration

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25 A TCP Primer in 10 Slides TCP is a reliable packet transfer protocol that uses a variable window algorithm for: – Error control – Flow control – Congestion control Two main algorithms (and a number of gadgets): – Slow start – Congestion avoidance

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26 Slow Start Algorithm Idea: –The new segment (packet) transmission rate adapts to the ACK reception rate –The TCP transmitter “tests” the link capacity At connection setup, cwnd = 1 segment (actually, cwnd=MSS) At every received ACK, cwnd = cwnd + 1 The resulting growth is exponential

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27 Slow Start Algorithm Host A 1 segment RTT Host B Time 2 segments 4 segments

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28 Slow Start: Sample Trace

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29 Congestion Avoidance Algorithm Idea: –Slower growth of cwnd At every ACK reception –cwnd = cwnd + 1/ cwnd –cwnd = cwnd + MSS*MSS/ cwnd (in bytes) The resulting growth is linear –cwnd grows by 1 MSS per RTT

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30 Congestion Avoidance Sample Trace

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31 When a Segment is Lost … …the transmitter rate has exceeded the available bandwidth Idea: –Reset the window size (cwnd=1) –Quickly recover the transmission rate The TCP transmitter detects the loss when the timeout expires, or 3 dupacks are received

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32 Graphically … 5 10 15 20 cwnd Time [RTT] ssthresh slow start congestion avoidance RTO

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33 TCP Fairness The congestion control algorithm in TCP is AIMD (additive increase, multiplicative decrease) Fairness: N TCP connections sharing one bottleneck link of capacity C, obtain each C/N

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34 R R Fair bandwidth sharing Throughput connection 1 Throughput connection 2 loss: window reduced by factor 2 congestion avoidance: AI Fairness with 2 TCP connections AI: linear increase MD: proportional decrease

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35 AQM: RED P(d) Avg min th max th 1 P max RED

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36 Consideration Accurate TCP models must consider: closed loop behavior short-lived flows multi-bottleneck topologies AQM schemes (or droptail) QoS approaches, two-way traffic,...

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37 Developing accurate analytical models of the behavior of TCP is difficult. A number of approaches have been proposed, some based on sophisticated modeling tools. Consideration

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38 Outline The Internet today Dimensioning IP networks GSPN and Queuing network models Fluid approaches Conclusions

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39 T. Lakshman and U. Madhow, "The performance of TCP/IP for networks with high bandwidth-delay products and random loss," IEEE/ACM Transactions on Networking, vol. 5, no. 3, 1997. M.Ajmone Marsan, E.de Souza e Silva, R.Lo Cigno, M.Meo, “An Approximate Markovian Model for TCP over ATM”, UKPEW '97 J. Padhye, V. Firoiu, D. Towsley, J. Kurose, "A Stochastic Model of TCP Reno Congestion Avoidance and Control“, UMASS CMPSCI Technical Report, Feb 1999. Literature

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40 C.Casetti, M.Meo, “A New Approach to Model the Stationary Behavior of TCP Connections”, Infocom 2000 M.Ajmone Marsan, C.Casetti, R.Gaeta, M.Meo, “An Approximate GSPN Model for the Accurate Performance Analysis of Correlated TCP Connections”, SPECTS 2000 M.Garetto, R.Lo Cigno, M.Meo, E.Alessio, M.Ajmone Marsan, “Modeling Short-Lived TCP Connections with Open Multiclass Queueing Networks”, PfHSN 2002 A.Goel, M.Mitzenmacher, "Exact Sampling of TCP Window States", Infocom 2002 Literature

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41 R.Gaeta, M.Sereno, D.Manini, "Stochastic Petri Nets models for the performance analysis of TCP connections supporting finite data transfer", QOS-IP 2003 R.Gaeta, M.Gribaudo, D.Manini, M.Sereno, "On the Use of Petri Nets for the Computation of Completion Time Distributon for Short TCP Transfers", ICATPN 2003 Literature

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42 1 2 3 4... N URLs/sec greedy flows finite flows (mice) finite flows greedy flows (elephants) IP core Problem statement

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43 Input variables: only primitive network parameters: IP network: channel data rates, node distances, buffer sizes, AQM algorithms (or droptail),... TCP: number of elephants, mice establishment rates and file length distribution, segment size, max window size,... Output variables: IP network: link utilizations, queuing delays, packet loss probabilities,... TCP: average elephant window size and throughput, average mice completion times,... Problem statement

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44 IP network sub-model TCP sub-model 1 load 1 load N packet loss probabilities, queuing delays TCP sub-model N decomposition of the whole system into subsystems: sub-models are built for groups of homogeneous TCP connections (same TCP version, similar RTT and routing,...) and for the IP network. iterative solution with FPA (Fixed Point Algorithm). Our modeling approach

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45 Our modeling approach

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46 GSPNs or. / G / queues describe states of the TCP protocol tokens or customers stand for TCP connections transition probabilities and service or firing times depend on TCP rules and network feedback (packet losses, round trip times,...) in the case of mice, colors or classes are introduced to represent the number of segments still to be transferred TCP sub-model

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47 TCP sub-model (Elephants)

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48 TCP sub-model (Mice)

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49 The IP network sub-model is an open queuing network, where each queue represents an output interface of an IP router, with its buffer of finite capacity. Different queuing models were tested: M / M / 1 / B: very simple, but only suitable when dealing with elephants and heavy load links M [D] / M / 1 / B: to better model the traffic burstiness of mice under variable link utilization M [D] / M [D] / 1 / B: a very accurate model, capable of coping with complex multi-bottleneck topologies IP network sub-model

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50 Bottleneck 1 Bottleneck 2 Numerical results: topology

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51 Numerical results: settings 0.1 0.5 1020100 0.4 length (segments) probability Packet size: 1000 bytes Buffer size: 64, 128, 512 packets Maximum TCP window size: 64 segments TCP tic: 0.5 s Flow length distribution (when mixing different flow lengths)

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52 model sim 20 40 60 80 100 120 N1 100 200 300 400 N2 2 3 4 5 6 Average window size Elephants crossing both bottlenecks

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53 model sim 20 40 60 80 100 120 N1 100 200 300 400 N2 0.01 0.1 Packet loss probability Elephants crossing both bottlenecks

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54 0 200 400 600 800 1000 N1 0 3000 6000 9000 12000 N2 0.01 0.1 Packet loss probability Elephants with increased channel data rates (100 Mb/s -- 1 Gb/s)

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55 0.001 0.01 0.1 0.750.80.850.90.951 Offered load Bottleneck 1 analysis - B = 128 analysis - B = 64 Mice (NewReno) Packet loss probability

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56 0.2 0.5 1.0 2.0 5.0 10 0.750.80.850.90.951 Average completion time (s) Offered load 10 packets 20 packets 100 packets Mice (NewReno)

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57 Outline The Internet today Dimensioning IP networks GSPN and Queuing network models Fluid approaches Conclusions

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58 V. Misra, W. Gong, D. Towsley, "Stochastic Differential Equation Modeling and Analysis of TCP Windowsize Behavior“, Performance'99 T. Bonald, "Comparison of TCP Reno and TCP Vegas via Fluid Approximation," INRIA report no. 3563, November 1998 V. Misra, W. Gong, D. Towsley, "A Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED“, SIGCOMM 2000 Literature

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59 Y.Liu, F.Lo Presti, V.Misra, D.Towsley, Y.Gu, "Fluid Models and Solutions for Large-Scale IP Networks", SIGMETRICS 2003 F. Baccelli, D.Hong, "Interaction of TCP flows as Billiards“, Infocom 2003 F.Baccelli, D.Hong, "Flow Level Simulation of Large IP Networks“, Infocom 2003 Literature

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60 Abandon a microscopic view of the IP network behavior, and model packet flows and other system parameters as fluids The system is described with differential equations Solutions are obtained numerically Modeling approach

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61 A simple example: One bottleneck link RED buffer Elephants only (no slow start) Modeling approach

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62 TCP model dW s (t)/dt = 1/R s (t) – W s (t) s (t) / 2 Where: W s (t) is the average window R s (t) is the average round trip time s (t) is the congestion indication rate of TCP sources of class s at time t

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63 IP network model dQ k (t)/dt = Σ s W s (t) (1-P(t)) / R s (t) – - C 1 {Qk(t)>0} Where: Q k (t) is the length of queue k at time t

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64 IP network model R s (t) = PD s + Q k (t)/C Where: PD s is the propagation delay for source s

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65 IP network model s (t+R s (t)) = W s (t)/R s (t) P(t) Where: P(t) is the loss probability at time t P(t) = RED(Q(t))

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66 Fluid models – work in progress Slow start (mice) Droptail buffers Finite window Threshold Distributions Fast recovery Core network topologies

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67 Fluid models – results

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68 Fluid models – results

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69 Fluid models – results

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70 Fluid models – results

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71 Fluid models – results

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72 Fluid models – results

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73 Fluid models – results

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74 Fluid models – results

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75 Fluid models – results

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76 Fluid models – results

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77 Fluid models – results

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78 Fluid models – results Baccelli and Hong obtained results for an access network with over one million TCP flows, about ten thousand routers, and link capacities from 6 Mb/s to 50 Gb/s.

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79 Outline The Internet today Dimensioning IP networks GSPN and Queuing network models Fluid approaches Conclusions

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80 Conclusions Fluid models today seem the most promising approach to study large IP networks Tools for the model development and solution are sought Fluid Petri Nets may be helpful for the model construction Efficient numerical techniques are a challenge

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81 Conclusions The modeling paradigms to study the Internet behaviour are changing This is surely due to scaling needs, but probably also corresponds to a new phase of maturity in Internet modeling Reliable predictions of the behavior of significant portions of the Internet are within our reach

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82 A comment on model complexity time models used understanding of mechanisms being modeled models proposed earlymiddle late model complexity Adapted from [Hluchyj 2001], [Kurose 2001] We need to go down

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83 Thank You !

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84 The second law of invited talks Careful with questions! The speaker knows no detail !

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