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Modeling client arrivals at access
points in wireless campus-wide
networks
Maria Papadopouli
Assistant Professor
Department of Computer Science
University of North Carolina at Chapel Hill (UNC)
This work was partially supported by the IBM Corporation under an IBM Faculty Award
2004
It was done while visiting the Institute of Computer Science, Foundation for Research and
Technology-Hellas, Greece
Coauthors And Collaborators
Haipeng Shen
Department of Statistics & Operations Research
University of North Carolina at Chapel Hill (UNC)
Spanakis Manolis
Institute of Computer Science
Foundation for Research and Technology - Hellas
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Roadmap
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Motivation & Research Objective
Summary of main contributions
Methodology
Modeling the client arrival
Clustering of access Points (APs)
Future Work
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Motivation & Research Objective
 Better admission control, load balancing, capacity
planning mechanisms
 More realistic access models for simulations &
performance analysis studies
 Evolution of wireless access
 Model client arrivals at wireless APs
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Data Set
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729-acre campus: 26,000 students, 3,000 faculty, 9,000 staff
Diverse environment
14,712 unique MAC addresses
488 APs (Cisco 1200, 350, 340 Series)
Syslog traces
Tracing period: 29 September-25 November 2005
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Main Contributions
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Novel methodology for modeling client arrivals
at wireless APs
Model of client arrivals at APs as time-varying
Poisson process
Use of SiZer visualization tool to understand
the internal structures of traces
Clustering of visit arrivals based on building
type
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SiZerMap of Visit Start Times (AP222)
increasing trend
decreasing trend
constant
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Visit Inter-arrival Times
(17:30-18:30)
decreasing trend
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Visit Inter-arrival Times
(Uniform Noise Added)
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Background on Poisson Process
Stochastic point process
that counts the number of events in [0,t]
• Arrival rate l
• Renewal process with inter-arrival times independent
exponential
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Analysis of Inter-arrival Times
Simulation envelope
sampling variability
 Strong autocorrelation of inter-arrival times  cannot model
visit arrival as a renewal process with independent Weibull interIEEE Lanman'05
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arrival times
Time-varying Poisson Process
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Arrival rate: function of time, λ(t)
Smooth variation of λ(t) is familiar in both theory
and practice in a wide variety of contexts
(e.g. when driven by human behaviors)
 Seems reasonable for client arrivals
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Construction of a Statistical Test
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Null hypothesis
The arrival process is a time-varying Poisson process with
a slowly varying arrival rate
Break up the interval of a day into short blocks (i=1,..,24)
Show that the null hypothesis cannot be rejected
Define (i slot, j arrival)
• Under the null hypothesis Rij will be independent standard exponential
variable
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Testing the Null Hypothesis
 Show the exponentiality of Rij
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Apply Kolmogorov-Smirnov test
Based on the maximum deviation between the
empirical cumulative distribution & hypothesized
theoretical CDF
Graphical tools
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Kolmogorov-Smirnov Test
The test statistic is 0.0188
 p-value of 0.15 with 2143 observations
p-value is large
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The null-hypothesis can not be rejected
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Exponentiality of Rij for [17:30, 18:30]
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Validation of Time-varying Poisson Models
Repeated the analysis and got similar
results
We analyzed
 A few other hours at AP 222 (academic)
 Three other hotspot APs of other building
types (library, theater, residential)
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Clustering Based on
Building Types & Client Arrivals
O 25-th percentile
x Median
 Std. Deviation
Aggregate Hourly Percentage of visits
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Summary
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Novel methodology for modeling the arrival of
clients at APs
Time-Varying Poisson processes model well
the client arrivals at APs
Validation of the models for different hours of
day and different APs
Cluster of APs based on the building type and
load of arrivals
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Future Work
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Model flow arrivals & cluster them based on client
profile, mobility & AP
Provide guidelines for load balancing, capacity
planning & energy conservation
Enhance traffic forecasting using flow information
Validate model with traces from other wireless
networks
Contrast models from different wireless environments
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More Info
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http://www.cs.unc.edu/~maria
http://www.ics.forth.gr/mobile/
[email protected]
Thank You!
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