a queuing theory approach to network path parameter estimation
DESCRIPTION
A Queuing Theory Approach to Network Path Parameter Estimation. Péter Hága Krisztián Diriczi Gábor Vattay István Csabai Attila Pásztor Darryl Veitch. Packet pair methods. - PowerPoint PPT PresentationTRANSCRIPT
A Queuing Theory Approach to Network Path Parameter Estimation
Péter Hága
Krisztián Diriczi
Gábor Vattay
István Csabai
Attila Pásztor
Darryl Veitch
CNL - Network Performance Measurement Group2
Packet pair methods
Sender Receiver
Sender Monitor: Receiver Monitor:
Goal: estimate network parameters (available bandwidth, physical bandwidth, cross traffic, etc.) with end-to-end methods
CNL - Network Performance Measurement Group3
Packet pair methods
• fluid model – the asymptotic behaviour is correct, but unable to describe the transition region
• new analytic description of the transition region
t2-t1 ’t2*-t1
*
CNL - Network Performance Measurement Group4
Outline
• The average of the output spacing• Explicit solution for M/D/1• Validation with packet level simulation• Parametrization with the granularity• Estimating the network parameters• Laboratory and Internet Experiments • Conclusion
CNL - Network Performance Measurement Group5
Output spacing
Assuming stationarity, the distribution of the output spacing is related to the conditional probability F(w,t|w0) of having queue length w at time t assuming the queue length is w0 at t = 0.
In our case t = , w = w2, w0 = w1+p.
Cross traffic model – M/G/1packet with size of Pi arrive with Poisson rate i
CNL - Network Performance Measurement Group6
Output spacing
where Pp(t) is the probability that the queue is not empty at time t:
Takács integrodifferential equation:
CNL - Network Performance Measurement Group7
Explicit solution for M/D/1
Simplest M/G/1 type case is an M/D/1 queue:
• fixed cross traffic packet size: P• Poisson rate:
CNL - Network Performance Measurement Group9
Validation with packet level simulation
M/D/1 queue
P=12000 bits
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Validation with packet level simulation
Trimodal packet size distribution
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Validation with packet level simulation
Uniform packet sizes between [0:12000] bits
CNL - Network Performance Measurement Group13
Parametrization with the granularity
exact form of the CT packet size distribution is not neccessary; the value of the granularity is enough.
Granularity – the effective CT packet size:
CNL - Network Performance Measurement Group14
Parametrization with the granularity
M/D/1 curves for:fixed packet size, P=800 bits – Pg = 800 bits,uniform dist, [0:12000] bits – Pg = 4272 bits,trimodal dist, real Internet params – Pg = 9786 bits
CNL - Network Performance Measurement Group15
Parametrization with the granularity
M/D/1 curves for:fixed packet size P=9786 bits – Pg = 9786 bits,uniform dist [7200:12000] bits – Pg = 9786 bits,trimodal dist, real Internet params – Pg = 9786 bits
CNL - Network Performance Measurement Group17
Laboratory experiments
bottleneck link 10 Mbps, cross traffic bandwidth was 4 Mbps, Pg=12000bits.fitted parameters: C = 10 Mbps, Cc = 3.7 Mbps Pg = 12000 bits, while 100 packet pairs were averaged.
bottleneck link 100 Mbps, average cross traffic bandwidth was 22 Mbps, Pg=12000 bits. fitted parameters: C = 100 Mbps, Cc = 22.5 Mbps Pg = 15000 bits.
CNL - Network Performance Measurement Group18
Internet measurements www.ETOMIC.org
ETOMIC nodes located in Birmingham, UKand Salzburg, Austria. estimated parameters: C = 1.7 Mbps, Cc = 0.1 Mbps and Pg = 15000 bits.
ETOMIC nodes located in Pamplona, Spain and Budapest, Hungary. estimated parameters: C = 100 Mbps,Cc = 58.2 Mbps and Pg = 9000 bits.
CNL - Network Performance Measurement Group19
Laboratory and Internet measurements
Comparision to existing tools: - pathload- pathChirp
data for our method - modified pathChirp tool.
CNL - Network Performance Measurement Group20
Summary
• new theoretical approach • new framework based on the Takács equation• exact formula for the average output spacing• granulatiry parameter = effective packet size,
the third important parameter in describing packet pairmeasurements
• confidence surfaces of the estimated parameters (C,Cc,Pg)• validation in real measurements in our testlab• validation in the ETOMIC infrastructure