# On the Use of Fixed Point Approximations to Study Reliable Protocols over Congested Links Michela Meo Michele Garetto Renato Lo Cigno Marco Ajmone Marsan.

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On the Use of Fixed Point Approximations to Study Reliable Protocols over Congested Links Michela Meo Michele Garetto Renato Lo Cigno Marco Ajmone Marsan Globecom 2003

Access link scenario Q clients servers λ c conn/s Arrival process of new connections data packets

Definition of “ g ”  The “normalized goodput” g (or “nominal link utilization”) on the link is defined as follows:  The actual traffic intensity  includes also retransmissions arriving at the link

 Only necessary retransmissions:

Un-necessary retransmissions: the  parameter

0.0001 0.001 0.01 0.1 1 0.80.850.90.9511.051.11.151.2 Average Packet Loss Probability ( p ) Traffic Intensity (  ) M/M/1/B B = 16 B = 32 B = 64 TCP g = 0.90 g = 0.95 g = 0.98 Convergence of the FPA (unique solution)

0.0001 0.001 0.01 0.1 1 0.80.850.90.9511.051.11.151.2 Packet loss probability ( p ) Load (  ) TCP - Link utilization (g) = 0.95 M/M/1/B (B = 32).

Convergence of the FPA (double solution) Stable point Unstable point

flow dist ~ geom (20) 0.0001 0.001 0.01 0.1 1 0.80.820.840.860.880.90.920.940.960.981 Average Packet Loss Probability (p) Normalized Goodput (g) flow dist ~ geom (600) flow dist ~ geom (60) 1 stable solution 1 unstable solution 1 stable solution Stability region ns simulations: B = 128

g = 0.986

Fig. 6

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