1. 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

2. IEEE Lanman'052 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

3. IEEE Lanman'053 Roadmap Motivation & Research Objective Summary of main contributions Methodology Modeling the client arrival Clustering of access Points (APs) Future Work

4. IEEE Lanman'054 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

5. IEEE Lanman'055

6. 6 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

7. IEEE Lanman'057 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

8. IEEE Lanman'058 SiZerMap of Visit Start Times (AP222) increasing trend decreasing trend constant

9. IEEE Lanman'059 Visit Inter-arrival Times (17:30-18:30) decreasing trend

10. IEEE Lanman'0510 Visit Inter-arrival Times (Uniform Noise Added)

11. IEEE Lanman'0511 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

12. IEEE Lanman'0512 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 envelope sampling variability

13. IEEE Lanman'0513 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

14. IEEE Lanman'0514 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

15. IEEE Lanman'0515 Testing the Null Hypothesis  Show the exponentiality of R ij Apply Kolmogorov-Smirnov test Based on the maximum deviation between the empirical cumulative distribution & hypothesized theoretical CDF Graphical tools

16. IEEE Lanman'0516 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

17. IEEE Lanman'0517 Exponentiality of R ij for [17:30, 18:30]

18. IEEE Lanman'0518 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)

19. IEEE Lanman'0519 Clustering Based on Building Types & Client Arrivals Aggregate Hourly Percentage of visits O 25-th percentile x Median  Std. Deviation

20. IEEE Lanman'0520 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

21. IEEE Lanman'0521 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

22. IEEE Lanman'0522 More Info http://www.cs.unc.edu/~maria http://www.ics.forth.gr/mobile/ maria@cs.unc.edu Thank You!