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Modélisation et Evaluation des Performances des Systèmes à Evénements Discrets

Modélisation et Evaluation des Performances des Systèmes à Evénements Discrets. Philippe Nain INRIA. Quelques dates. 1917: Travaux Erlang Probabilité de débordement. 1957: Réseaux à forme produit de Jackson.

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Modélisation et Evaluation des Performances des Systèmes à Evénements Discrets

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  1. Modélisation et Evaluation des Performances des Systèmes à Evénements Discrets Philippe Nain INRIA

  2. Quelques dates 1917: Travaux Erlang Probabilité de débordement 1957: Réseaux à forme produit de Jackson 1975-76: Réseaux BCMP, Réseaux de Kelly Modélisation du réseau Arpanet (Kleinrock) Années 80: Logiciels dédiés (QNAP2, PAW, etc.). Evaluation de protocoles (Ethernet, FDDI, etc.) Années 90: Bande passante équivalente Nature <<fractale>> du trafic IP Network calculus

  3. Quelques dates (suite) • 2000  : Les années ... TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP, TCP

  4. Modélisation de TCP Mode slow start : W <-- W + 1 à chaque ACK reçu W <-- W/2 si perte TD W <-- 1 si perte TO Mode congestion avoidance : W <-- W + 1/W à chaque ACK reçu W <-- W/2 si perte TD W <-- 1 si perte TO

  5. Modélisation de TCP (suite) X(t) =Taille de la fenêtre de congestion à l ’instant t X(t) Linear increase at rate Congestion detection Multiplicative decrease (by n) X(n+1) X(n) X(n+2) S(n) S(n+1) t T(n) T(n+1)

  6. Modélisation de TCP (suite) X(n) = Taille de la fenêtre juste avant T(n) S(n) = T(n+1) - T(n) ;  = 1/E[S(n)] R(k) = Cov(S(n),S(n+k)) X(n+1) =  X(n) +  S(n) [Altman, Avratchenkov, Barakat --Sigcomm ’00]:

  7. Modélisation de TCP (suite) Une autre façon de voir le même résultat: • p = Probabilité de perte ( ) • RTT = Round-trip time ( )

  8. Modélisation de TCP (suite) Pertes <<déterministes>> (S(n)  1/;  = 0.5 TCP Reno) Pertes <<Poisson>> (P(S(n) < x) = 1-exp(-x),  = 0.5)

  9. Modélisation de TCP (suite) Autres approches possibles : • Algèbre max-plus [Baccelli, Hong-- Sigcomm ’00]  Modèle discret • Equation différentielle stochastique [Misra, Gong, Towsley -- Sigcomm ’01]  Modèle fluide • Etc.

  10. Modélisation de TCP (suite) Extensions du modèle : • Timeouts • Borne sur la fenêtre d ’émission • Calcul des moments d ’ordre supérieur • Etc. Verrou : • Session TCP courte durée

  11. Diffserv Architecture marking r b scheduling . . . End host: - Negociates a profile with edge router Edge router: - Per-flow traffic management - Marks packets as in-profile and out-profile Core router: - Per class traffic management - Buffering and scheduling based on marking at edge - Preference given to in-profile packets - Assured Forwarding

  12. Leaky-Bucket Marking at Edge • Profile: Pre-negotiated rate A, bucket size B • Packet marking at edge based on per-flow profile Rate A B User packets

  13. Assured Forwarding at Core • Active queue management • Maintains average queue length, x • Compute • p1: drop prob. of a green pkt • p2: drop prob. of a red pkt 1 Dropprob p2 p1 Avg. queue length, x

  14. TCP over AF Service Profile: A,B • Questions: • Is it possible to provide a TCP flow a fixed (minimum) rate through proper choice of parameters (A,B) • Is it possible to provide service differentiation across a set of TCP flows? • Determine “achieved throughput” r [Sahu, Nain, Towsley, Firiou, Diot -- Sigmetrics’00] Marker Bottleneck core TCP Other flows

  15. Our Approach: Simple Loss Model p2 p2 p1 • Non-overlapping loss model • if p2 < 1p1 = 0; under-subscribed case • if p1 > 0p2 = 1; over-subscribed case • Derive • “achieved rate” for each case separately • Conjecture • overlapping loss model reduces to one or the other 1 Dropprobability Avg. queue length x

  16. TCP Throughput: A Simple Deterministic Model W(t) Marked green • Define assured window size, Wa: Wa = A x T, where T is a constant round trip time • W, avg. window size at the begin of a cycle • 2W, avg. window size just prior to a loss event Tokens accumulate 2W Wa W • Under-subscribed case:p1=0, p2<1 • Avg. number of red packets prior • to first loss: 1/p2 • Under-subscribed case:p1=0, p2<1 • Avg. number of red packets prior • to first loss: 1/p2 • Equate • Achieved rate, r = 3 W/ 2 T Time t

  17. TCP Throughput: A Simple Deterministic Model(cont’) Over-subscribed case: p1>0, p2=1 W(t) marked green • Red packet loss: 2W Wa W tokens accumulate • Green packet loss: • Avg. number of green packets prior to first loss: 1/p1 • Equate Time t • Sending rate is

  18. Simulation/Experiments To validate analytical model • Ns-2 simulation • Testbed implementation • implemented various packet marking and multi-RED on Linux 2.2.10 kernel • Model validation • round-trip time 100~400ms • wide range of loss rates • Bernoulli loss model • buffer overflow • large number of TCP flows Sprint ATL Testbed Configuration

  19. Sample Validation Results Under-subscription case Over-subscription case A = 100kb/s, B=20, T=100ms A=1000kb/s, B=64, T=100ms

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