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HET-NETs 03 FIRST INTERNATIONAL WORKING CONFERENCE ON PERFORMANCE

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HET-NETs 03 FIRST INTERNATIONAL WORKING CONFERENCE ON PERFORMANCE Powered By Docstoc
					IP Network Traffic Measurement and Modelling
Presented to the COST 282 MCM meeting on 24-25 September 2003, Istanbul
Dr. Zhili Sun and Mr. Lei Liang Centre for Communication System Research University of Surrey Guildford Surrey GU2 7XH Z.Sun@surrey.ac.uk

Objectives
 To study IP network traffic by measurement .  To find mathematical formula to fit the measurement results  So that the formula will be used for traffic modelling to capture the relevant network traffic features, attributes, and characteristics

Traffic Measurement Parameters


QoS parameters for traffic engineering include:
  

delay, jitter and packet loss





IETF IPPM working group tries to define metrics of these parameters Traffic parameters at packet level includes:


Throughput, packet length, packet interarrival time, packet burstness and so on



Packet interarrival time is measured in this paper.
ArrivalInterval  ArrivalTime(i)  ArrivalTime(i  1)

Parameter Measurement Algorithm


In each measurement, packets are classified in terms of flow direction.


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Uplink stream: packets from local machine to remote servers Downlink stream: packets from remote servers to local machine

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

Two direction flows are expected to have different performances and characteristics. The TCP traffic of the measurement node generated by FTP applications was measured

Packet capture method
Customer application Text file

WinPcap

Capture filter Capture driver Network adpater
Packet flow

Ethernet

Packet Interarrival Time Analysis






Downloading files always produces very small interarrival time Either for downloading small file or big file, the RTT has significant effect on the packet interarrival time The file size affects the FTP packet interarrival time

Fitting Using Pareto+Pareto Distribution

Fitting Using Pareto+Rayleigh Distribution

FTP Packet Interarrival Time Formula (1/3)


It has been found that there is no standard distribution can fit well to the measured distributions of the interarrival time for both small and big file downloading.




Pareto distribution fits the measurement curve very well around 0 second Sharp rise cuts off the distribution around the RTT point



Two different standard distributions were combined to model this kind of cut-off distributions.


It should guarantee the final distribution
FX ( x)   f X ( x)dx  1
k 

f X (x) has

a CDF:

xk

FTP Packet Interarrival Time Formula (2/3)


For the small file download, the rise is very sharp. To model this distribution, we chose Pareto+Pareto distribution as the ideal model.
 c1Tmin c1  c1 1  f T (t )   t c c 2TRTT 2   t c2 1 
TRTT c

Tmin  t  TRTT TRTT  t  Tmax

and

c1Tmin 1   1   c1 1 dx Tm in t

where TRTT is the cut-off point. Tmin and Tmax is the minimum and maximum
value of the FTP packet interarrival time respectively.

FTP Packet Interarrival Time Formula (3/3)


It was found that Pareto+Rayleigh distribution could model the packet interarrival time very well for big file case.
   f T (t )      cTmin t c 1  t2  t exp  2  2  2b  b  
TRTT
c

Tmin  t  TRTT TRTT  t  Tmax
c

and

c1Tmin 1   1   c1 1 dx Tm in t

where TRTT , Tmin and Tmax are the same as previous page.

WIDE Backbone Traces




To verify the method described in above paragraphs, more analysis was executed to 6 TCP traces provided by the MAWI (Measurement and Analysis on the WIDE Internet) Working Group The 6 traces we used in our analysis were collected at an IPv6 line connected to WIDE-6Bone in this January and February
 

Totally contain around 6 million TCP packets All of the traces were captured using a software named TCPDUMP.EXE and saved in dump file format. Arrival time stamp of each TCP packet in the 6 traces was extracted to calculate the packet interarrival time

WIDE Backbone Traces Information
Traces Measurement Interval (Seconds) No. of TCP Packets TCP Packet Volume (Bytes)

Tue., 14 Jan. 2003

15428.03

1778766

2352426690

Mon., 20 Jan. 2003

46129.84

1546850

1036843860

Sun., 26 Jan. 2003

64799.24

608914

113541437

Sun., 02 Feb. 2003

64799.20

855893

263516579

Tue., 11 Feb. 2003

64798.06

871386

227649654

Fri., 28 Feb. 2003 Total

14063.15 270017.52

240541 5902350

51718205 4045696425

Traces Analysis


All of the traces have a common characteristic. All of their packet interarrival time CDFs have sharp cut-off around 0.11 second


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The cut-off appears more outstanding when the TCP traffic is less loaded Might be a pair of hosts constantly communicate through the measurement point that contributes a significant fixed RTT during all of the capture intervals

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This cut-off phenomenon implies that a combination of more than one well-known distribution should be used to model the measured results

TCP Traces Modelling

TCP Traces Modelling formula
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Two Inverse Gaussian CDFs connected at the cut-off point could fit the measurement curve reasonably well
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Inverse Gaussian Plus model

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We can mathematically represent the TCP packet interarrival time using the following PDF formula
1    w1 (t  u1 ) 2   w1  2  exp   2  2t 3  2u1 t     f T (t )   1   w2  2   w2 (t  u 2 ) 2      3  exp  2 2u 2 t   2t    

Tmin  t  TCUT TCUT  t  Tmax
 dt , TCUT is the cut-off 

  w1 (t  u1 ) 2  w1  exp  Where   1    2 2t 3  2u1 t   Tm in 
TCUT

1 2

point, Tmin and Tmax are the minimum and maximum interarrival time respectively

Conclusions


 

The packet interarrival time distribution of the IP traffic is sensitive and affected by RTT that causes a cut-off point on the curve. Need to use two distribution functions to fit the data Regarding the difference caused by the size of transported file, two models were established for FTP packet interarrival time distribution.
 

For transmitting small files: Pareto+ Pareto model For transmitting big files: Pareto+Rayleigh



The modelling algorithms is also use to fit 6 backbone traces from public domains