1. Spatio-Temporal Modeling of Traffic Workload in a Campus WLAN
Felix Hernandez-Campos Merkouris Karaliopoulos Maria Papadopouli 1,2, Haipeng Shen2
1 Foundation for Research & Technology-Hellas (FORTH) & University of Crete
2 University of North Carolina at Chapel Hill
3 Google
1IBM Faculty Award 2005, EU Marie Curie IRG, GSRT “Cooperation with non-EU countries” grants

2. Motivation Growing demand for wireless access
Mechanisms for better than best-effort service provision need to be deployed
Examples:
capacity planning, monitoring, AP selection, load balancing
Evaluate these mechanisms via simulations & analytically
Models for network & user activity are fundamental requirements

3. Wireless infrastructure
disconnection
Internet
Router
Wired
Network
AP3
Switch
Wireless
Network
User A
AP 1
AP 2
User B

4. Wireless infrastructure
Internet
disconnection
Router
Wired Network
Switch
AP3
Wireless
Network
User A
AP 1
AP 2
roaming
roaming
User B
Session
Associations 1 2 3
Flows
Packets

5. Modeling Traffic Demand
Multi-level spatio-temporal nature
Different spatial scales
Entire infrastructure, AP-level, client-level
Time granularities
Packet-level, flow-level, session-level

6. Modelling objectives
Distinguish two important dimensions on wireless network modelling
User demand (access & traffic)
Topology (network, infrastructure, radio propagation)
Find concepts that are well-behaved, robust to network dependencies & scalable

7. Internet Wired Network Switch Wireless Network Events disconnection
Router
Switch
AP3
Wireless
Network
User A
AP 1
AP 2
Events
User B
Session 1 2 3
Association
Flow
Arrivals t1 t2 t3 t4 t5 t6 t7
time

8. Our Models Session Arrival process Starting AP Flow within a session
Number of flows
Size
Systems-wide & AP-level
Captures interaction between clients & network
Above packet level for traffic analysis & closed-loop traffic generation

9. Wireless Infrastructure
488 APs, 26,000 students, 3,000 faculty, 9,000 staff over 729-acre campus
SNMP data collected every 5 minutes
Packet-header traces:
8-day period April 13th ‘05 – April 20th ‘05
175GB
captured on the link between UNC & the rest of the Internet using a high-precision monitoring card
captured on the link between UNC and the rest of the Internet using a high-precision monitoring card (Endace DAV 4.3GE)

10. Time Series on Session Arrivals

11. Session Arrivals Time-varying Poisson Process
The interarrival times for the Poisson process are i.i.d exponential random variables. A natural generalization is to consider a counting process for which the interarrival times are i.i.d with an arbitrary distribution. Such process is called a renewal process.
The top figure shows an exponential quantile plot of the R_{I,j} during one randomly chosen hour. The bottom figure shows the autocorrelations of the Rij up to 20 lags. The sample autocorrelation are always within the confidence interval, so the Rijs do not exhibit any significant correlations. We got similar results when repeating the same analysis for other one-hour intervals of the 8day dataset.
If you add simulation envelope, then each line is plotting the quantiles of a simulated data vs. the empirical data. The simulation data is generated from the distribution of interest using parameters (not necessarily the mean/sd, in the case of Bipareto and some other dist) estimated from the empirical data. This should be the most novel way to check a distribution. The R^2 measure used in CS literature is not as strong as this technique.

12. AP Preference Distribution
The original data, show in in red, lie within the natural variability of the lognormal model, since they remain within the blue simulation envelop. The only departure from lognormality is for the smallest values, i.e., for APs that more rarely serve as session-starting APs, hence featuring very small number of samples. Overall, the lognormal distribution is an excellent description of the data. We have also considered other models but they are clearly outperformed by the lognormal fit. For example, Zipf’s law, a classic way of describing popularity, is very far from the AP-preference distribution in our data

13. Number of Flows Per Session

14. Stationarity of the Distribution of Number of Flows within Session
We found consistent tails for the eight days suggesting that weekly periodicities are not critical for modelling the number of flows per session.

15. Flow Inter-Arrivals within Session
The simulation envelop is very narrow in this case, and shows that some deviations from the lognormal model I the upper part are significant. While more complex models, e.g., an ON/OFF model, may provide a better approximation, our lognormal fit certainly provides a reasonable description of the data using only two parameters.

16. Flow Size Model
We have also examined the stationarity of the flow size distributions over different days. We found consistent tails for the eight days suggesting that weekly periodicities are not critical for modelling the flow sizes.
The pareto distributon has two parametres a>0 and k>0 that are the decay exponent and scale parameters, respectively. The scale prameters also the minimum possible value of the random variable.
Similar parameters has the bipareto. The tail distribution initiall decays as a power law with exponent a>0. Then, in the vicinity of a breakpoint kb, the decay exponent gradually changes to b>0.

17. Model Validation Methodology
Produced synthetic data based on
Our models on session and flows-per-session
Session arrivals: Time-Varying Poisson
Flow interarrival in session: Lognormal
Compound model (session, flows-per-session)
Flows interarrival in session: Weibull
Flat model
No session concept
Flows: renewal process
Given the heavy-tailed session duration, we impose simulation times in the order of days. In particular, we let the simulator synthesize traffic over a 3-day interval (simulation time), and process the measured traffic variables obtained in the third day.

18. Model Validation Methodology
Simulations -- Synthetic data vs. original trace
Metrics: Variables not explicitly addressed by our models
Aggregate flow arrival count process
Aggregate flow interarrival time-series (1st & 2nd order statistics)
 Systems-wide & AP-based
 Different tracing periods (in 2005 & 2006)
Given the heavy-tailed session duration, we impose simulation times in the order of days. In particular, we let the simulator synthesize traffic over a 3-day interval (simulation time), and process the measured traffic variables obtained in the third day.

19. Simulations Produce synthetic data based on aforementioned models
Synthesize sessions & flows for a 3-day period in simulations
Consider flows generated during the third day (due to heavy-tailed session duration)

20. Validation Number of Aggregate Flow Arrivals
Depicts the number of aggregate flow arrivals within intervals of one hour. The 2-level model tracks closely the original trace in this respect, and certainly better than the other two approaches, although, it overestimates the arrivals during the busy hours. The compound model yields less satisfactory matching, although, it can respond to the non-stationarity of flow arrivals thanks to its provision for time-varying Poisson session arrivals. On the contrary, the flat model cannot respond to the time variations of flow arrivals, since the emiprical distribution is estimated over the full trace and averages the hourly fluctuations of the traffic demand.

21. Validation Coefficient of Variation

22. Validation: Autocorrelation

23. Aggregate Flow Inter-arrivals
We found that the flow interarrivals within a session follow a lognormal distribution; the compound model with the transformed Weibull variables cannot give an equally good fit for these interarrivals and this is is reflected in the aggregate flow interarrival data.
99.9th percentile

24. Related Work in Modeling Traffic in Wired Networks
Flow-level
in several protocols (mainly TCP)
Session-level
FTP, web traffic
Session borders are heuristically defined by intervals of inactivity

25. Related work in Modeling Wireless Demand
Flow-level modelling by Meng et al. [mobicom04]
No session concept
Flow interarrivals follow Weibull
Modelling flows to specific APs over one-hour intervals
Does not scale well

26. Conclusions
First system-wide, multi-level parametric modelling of wireless demand
Enables superimposition of models for demand on a given topology
Focuses on the right level of detail
Masks network-related dependencies that may not be relevant to a range of systems
Makes the wireless networks amenable to statistical analysis & modeling

27. Future Work
Explore the spatial distribution of flows & sessions at various scales of spatial aggregation
Examples: building, building type, groups of buildings
Model the client dynamics
The collected SNMP data do not include all information required for our two-level modelling approach

28. UNC/FORTH Web Archive  Login/ password access after free registration
Online repository of
wireless measurement data
models
tools
Packet header, SNMP, SYSLOG, signal quality
 Login/ password access after free registration
Joint effort of Mobile Computing UNC & FORTH

29. WitMeMo’06 2nd International Workshop on
Wireless Traffic Measurements and Modeling
August 5th, 2006
Boston