Fixed-Point Models for the End-to-End Performance Analysis of IP by warrent

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									Fixed-Point Models for the End-to-
End Performance Analysis of IP
Networks

     R. J. Gibbens., S. K. Sargood, C. Van Eijl, F.
     P. Kelly., H. Azmoodeh, R. N. Macfadyen, N.
     W. Macfadyen
Abstract

   Presents an approach to modeling end-to-
    end performance for IP networks.
   Consider adaptive behavior of TCP/IP,
    instead of a constant rate
   Fixed-point method which determines packet
    loss, link utilization and TCP throughput
    across the network.
Fixed-Point Equations with Open Source

   α1r and α2r: Offered arrival rates for high and low
    priority traffic streams on a directed route r
   L1j and L2j: Loss probabilities at each resource (link)
    (j =1, 2, …, J)
   Assume independence of the links…
   Then the load at link j is
Fixed-Point Equations with Adaptive
Source
   Relating loss prob and TCP throughput


       If there is a rate limit R, then take the minimum of S and R

   nir: # of TCP sessions of type i in route r. Assumed to be i.i.d
    Poisson distributed, which results from the M/G/∞ model for TCP
    sessions suggested by Paxson and Floyd [1].


   End-to-end packet loss prob satisfies




    [1] V. Paxson & S. Floyd, "Wide Area Traffic: The Failure of Poisson
    Modelling," IEEE/ACM Transactions on Networking, Vol. 3 No. 3, pp. 226-
    244, June 1995.
Resource model

   M/M/1/K queue with buffer size B
   Reject a low priority packet if there are T or more
    packets already in the buffer
   The transition rate of the Markov Chain is


   So the equilibrium distribution is
   The loss probs and delays
Example Network with Adaptive Sources

   Topology and equations
Example Network with Adaptive Sources

   Loss prob & Throughput




     Mean # of sessions      Mean # of sessions
Modeling IP Backbone Network
Topologies
   18 core routers, 9 access routers and 86 unidirectional links
    (100Mbps LAN access-core router interconnects, and ‘long-
    distance’ core router WAN links which are STM-1s, 155.52
    Mbps)
   Routes are computed off-line
   41 routes (between access routers) with offered loads 7.5~60
    Mbps (for open source model), and high and low priority traffic is
    30:70.
   For adaptive source model, the mean # of TCP sessions is
    computed by assuming
     300kbps/session for high priority traffic

     100kbps/session for low priority traffic.

   Buffers: 32 packets, mean packet size: 500Bytes; low priority
    traffic discard threshold: 16.
Modeling IP Backbone Network
Topologies
   Topology
Results of the IP Backbone Network

   Open source model
     For this traffic demand, link utilization and packet loss are low on
      most links.
   Adaptive source model
     Links had a higher utilization for the case of TCP without rate
      limits than with a 1Mbps rate limit
     The link from mil_c2 to zur_c2 had the second highest loss of
      high priority packets at 0.5%, since the small RTT from Milan to
      Zurich leads to high throughput.
     In the Milan-Zurich route, imposing a rate limit of 1 Mbps on all
      sources causes the mean throughput of high priority traffic to fall
      by a factor of 4, but the mean throughput of low priority traffic to
      rise by a factor of ~10.
Discussion

   Link independence assumption
   Throughput is not in explicit form (which may
    be difficult)

								
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