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
Arrival process of new
connections
λc conn/s
Q
clients
data packets
servers
Access link scenario
Ingoing traffic
Outgoing traffic
Uncongested link:
Congested link:
Definition of “g”
 The “normalized goodput” g (or “nominal link
utilization”) on the link is defined as follows:
g
λc flows/s x average flow size bits
link capacity bits/s
 The actual traffic intensity  includes
also retransmissions arriving at the link
 Only necessary retransmissions:
 Addition of un-necessary retransmissions:
Un-necessary retransmissions:
the  parameter
Convergence of the FPA (unique solution)
Average Packet Loss Probability ( p )
1
0.1
g
ρ
1 p
g = 0.90
g = 0.95
g = 0.98
TCP
0.01
M/M/1/B
 B (1   )
p
1   ( B 1)
0.001
0.0001
0.8
B = 16
B = 32
B = 64
0.85
0.9
0.95
1
1.05
Traffic Intensity (  )
1.1
1.15
1.2
Convergence of the FPA (unique solution)
Packet loss probability ( p )
1
0.1
TCP - Link utilization (g) = 0.95
g
ρ
1 p
.
0.01
M/M/1/B (B = 32)
 B (1   )
p
1   ( B 1)
0.001
0.0001
0.8
0.85
0.9
0.95
1
Load (  )
1.05
1.1
1.15
1.2
Convergence of the FPA (double solution)
Unstable point
Stable point
Stability region
Average Packet Loss Probability (p)
1
B = 128
ns simulations:
g
flow dist ~ geom (20)
0.1
flow dist ~ geom (60)
1
1
flow dist ~ geom (600)
0.01
1 stable solution
1 unstable solution
0.001
1 stable solution
0.0001
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
Normalized Goodput (g)
0.96
0.98
1
g = 0.986
Fig. 6
0.1
model - constant b
b=1
b=2
b=3
b=4
b=5
0.01
sim - average flow size (packets)
20
60
600
0.001
0.9
0.92
0.94
0.96
Normalized Goodput (g)
0.98
1