On XCP Stability in a Heterogeneous Network

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On XCP Stability in a Heterogeneous Network

• ? Yusuke Sakumoto
• Hiroyuki Ohsaki
• Makoto Imase
• Graduate School of
• Information Science and
• Technology,
• Osaka University, Japan

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Contents

• Introduction
• XCP (eXplicit Control Protocol)
• Research Objectives
• Stability analysis
• Numerical Examples
• Effect of parameters on stability of XCP
• Conclusion and future work

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Background

• Several problems in TCP Reno
• A large number of packets are discarded
• Caused by inability of source hosts to detect
  congestion before some packets are lost
• Transport-layer communication protocols are
  proposed
• Use explicit feedback from a router to end hosts
• XCP has been receiving attention

Efficiency data transfer
Explicit feedback
Router
End host
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Congestion Control Algorithm of XCP
5. receive packet copy feedback to ACK packet
1. store in congestion header
3.calculate feedback value(3)
2.send packet
6. receive ACK packet modify window size 200
3 ? 203
4.overwride feedback(3)
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XCP Router Algorithm

• Composed of efficiency controller and fairness
  controller
• Calculates the amount of rate increase/decrease
  for each XCP flow

efficiency controller(try to maximize
utilization of the router)
fairness controller(try to realize
fairnessamong competing XCP flows)
S T A R T
E N D
yes
calculates f (the total amount of
rateincrease/decrease for all XCP flows)
equally distributes f to all XCP flows
f?0?
no
proportionally distributesf to all XCP flows
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Related Works
8 D.Katabi, M.Handley and C.Rohrs, Congestion
Control for high bancwidth-delay product
networks, in Proceeding of ACM SIG- COMM
2002, vol.32, pp.89-102, Aug. 2002

• Simulation experiments 8
• XCP achieves better performance than TCP Reno
  does
• Characteristics of XCP have not been clarified
• Such as stability, transient performance
• Stability analysis 8
• Assume an identical propagation delay for all XCP
  flows
• Stability of XCP has not been sufficiently
  clarified
• Propagation delays of XCP flows must be not the
  same in real network

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Research Objectives

• Analyze stability of XCP in a heterogeneous
  network
• Model a network with heterogeneous XCP flows
• Use fluid-flow approximation
• Derive the conditions
• XCP control parameters should satisfy for stable
  XCP operation

XCP flow
XCP flow
delay50ms
Quantitatively investigate effect of system
parameters and XCP control parameters on
stability of XCP
delay30ms
delay70ms
XCP flow
XCP flow
heterogeneous network
fluid-flow approximation model
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Analytic Model
XCP flows are classified into flow classes, in
which XCP flows have the identical propagation
delay
flow class 1
flow class 2
flow class M
network with heterogeneous XCP flows with
different propagation delay sharing the single
bottleneck link
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Fluid-flow Model of XCP

• Model as discrete-time models with slot length of
  ?
• The transfer rate of XCP flows in flow class i
  at slot k1
• The current queue length of XCP router at slot
  k1

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Stability Analysis

• 1. Linearize the fluid-flow approximation model
• ? Analyze the stability of XCP around its
  equilibrium point
• 2. Introduce a state vector x(k)
• x(k) is composed of state variables
• State variable transfer rate, current queue
  length
• 3. Derive a state transition matrix M
• 4. Calculates the maximum modulus ?max of M
• The system is stable if ?max lt 1

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Numerical Examples
N1, N2 number of XCP flows t1,t2 two-way
propagation delay C output link bandwidth a,
ß, ? XCP control parameter

• Show only results in the case of two flow classes
• Investigate the effect of
• Propagation delays of XCP flows
• Variation in propagation delays of XCP flows
• Output link bandwidth C

t1
XCP source
N1
a ß ?
XCP source
XCP source
XCP source
C
N2
XCP source
XCP source
t2
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Analysis Result Effect of Propagation Delays of
XCP Flows
N1 N2

• Stability region of XCP control parameters (a?ß)

Stability region in a heterogeneous case
islarger than that in the homogeneous case
In the homogeneous cases, the stability region
is independent of two-way propagation delays
When XCP flows are heterogeneous, XCP operates
more stably than the case when XCP flows are
homogeneous
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Analysis Result Effect of Variation in
Propagation Delays of XCP Flows
t1 10ms, t2 20ms

• Stability region of XCP control parameters (a?ß)

Stability region is smallest when N1 is larger
than N2
When variation in propagation delays of XCP
flows are large, operation of XCP becomes less
stable
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Analysis ResultEffect of Heterogeneity in XCP
Flows
t1 10 ms, N2 1

• Maximum modulus ?max vs. Number of XCP flows N1

?max gt 1.0 (the operation of XCP becomes unstable)
The operation of XCP becomes unstable when N1
reaches around 100 for t2 200ms
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Ns2 Simulation ResultEvolutions of Window Size
of XCP Flows
When t2 200ms, window size showoscillatory
behavior
N1 99, N2 1
When the variation in propagation delays of XCP
flows is large, the window size of the XCP flows
become unstable
flow class 1
flow class 2
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Conclusion

• Analyze stability of XCP in a heterogeneous
  network
• Investigate effect of parameters on stability of
  XCP
• 1. When XCP flows are heterogeneous, XCP
  operates more stably than the case when XCP
  flows are homogeneous
• 2. When variation in propagation delays of XCP
  flows are large, operation of XCP becomes less
  stable

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Future Work

• Analyze the transient performance of XCP
• Utilize our fluid-flow model of XCP
• Derive the optimal configuration of control
  parameters
• Maximize the performance of XCP
• Based on stability analysis and transient
  analysis

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• Thank you for your kind attention