Modeling client arrivals at access points in wireless campus-wide networks

Maria Papadopouli Assistant Professor Department of Computer ScienceUniversity 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

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Coauthors And Collaborators

Haipeng ShenDepartment of Statistics & Operations ResearchUniversity of North Carolina at Chapel Hill (UNC)

Spanakis ManolisInstitute of Computer Science

Foundation for Research and Technology - Hellas

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Roadmap

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

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

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 • Renewal process with inter-arrival times independent exponential

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Analysis of Inter-arrival Times

Strong autocorrelation of inter-arrival times cannot model visit arrival as a renewal process with independent Weibull inter-arrival times

Simulation envelopesampling variability

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Time-varying Poisson Process

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 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

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

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

Aggregate Hourly Percentage of visitsO 25-th percentilex Median Std. Deviation

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Summary

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

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

http://www.cs.unc.edu/~maria http://www.ics.forth.gr/mobile/ maria@cs.unc.edu

Thank You!