m. papadopouli 1,2,3, m. moudatsos 1, m. karaliopoulos 2 1 institute of computer science, forth,...

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M. Papadopouli 1,2,3 , M. Moudatsos 1 , M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina, Chapel Hill, United States 3 University of Crete, Heraklion, Crete, Greece Modeling roaming in large-scale wireless networks using real measurements IEEE WoWMoM ’06, 1 st EXPONWIRELESS WORKSHOP, Niagara Falls, NY, 26 June 2006

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Page 1: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

M. Papadopouli1,2,3, M. Moudatsos1, M. Karaliopoulos2

1Institute of Computer Science, FORTH, Heraklion, Crete, Greece2University of North Carolina, Chapel Hill, United States

3University of Crete, Heraklion, Crete, Greece

Modeling roaming in large-scale wireless networks using real measurements

IEEE WoWMoM ’06, 1st EXPONWIRELESS WORKSHOP, Niagara Falls, NY, 26 June 2006

Page 2: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Outline

Background - Motivation

Wireless infrastructure

Measurement data

Describing wireless network access with graphs

– Graph definition/generation

– Graph properties

Current work

Page 3: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Background in WLAN arena

Desire to support real-time services – QoS provision challenges

Integration with other wireless networks– Mobile cellular networks

– Wireless backbone for other wireless nets (e.g., Personal Networks)

Standardization efforts to support/enhance control and management-plane functions

– IEEE 802.11k

– IETF CAPWAP WG

Page 4: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Motivation

Real measurement data are critical to system engineering

– Understand system dynamics, traffic & user access patterns, weaknesses & deficiencies

– Derive models for the user activity and the network

input to system engineering tasks and performance analysis

Challenge: identify trends/principles/rules that hold independent of the specific infrastructure

– Need for validation: describe findings, apply to other datasets, compare with others’ findings

This study uses measurement data to come up with an alternative description of the UNC network and the user access patterns

Page 5: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

UNC wireless infrastructure

Over 750 APs

– Steady growth :460 (Oct 04), 570 (Apr 05), 640 (Sep 05), 750 (May 06)

Spread amongst over 110 buildings

– Primarily academic, residential, administrative and clinical

40,000 users

– 10,000 different clients were logged in the traces

– Clients almost exclusively laptops or PDAs

Page 6: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Measurement data

Relied on Syslog messages

– Syslog agents activated in the APs

– Server on a dedicated host collects the data

– 24/7 process

Syslog messages log down several events

– Client (re/de)association, (de)authentications, roaming (transition between two APs)

Page 7: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

SYSLOG message generation

UNC Wired Network

Wireless Network

Router

Internet

User i AP 1 AP 2 User D

AP3Switch

: SYSLOG message(s)

User j

1

time t1

User j association

2

time t2

Roaming to AP2

disconnection

time t4

4

time t3Roaming to AP3

3

Page 8: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Roaming activity as a graph

AP i node i V

Client transition between APs edge between corresponding nodes

– Directed graph: (i,j) E when client transition from AP i to AP j

– Undirected graph: (i,j) E when client transition in either direction

– Weight of edge (i,j) : # client transitions from AP i to AP j

Function of the tracing period T, GΤ = (VT, ET)

In the paper, T = 1 week– 3 different weeks are studied : 17-24 Oct 04, 2-9 Mar 05, 13-

20 Apr 05

Graph G = (V, E)

Page 9: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Degree of connectivity (DoC)

Distribution of degree of connectivity

– Indegree, outdegree (directed graph)

– Degree (undirected graph)

Goodness-of-fit tests

– Visual tests (quantile-quantile plots)

– Statistical tests

Evolution of DoC with time

Page 10: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

DoC – visual goodness-of-fit tests

Several discrete distributions tested– Negative Binomial

– Geometric

– Binomial

– Poisson

ML estimation of parameters for the statistical tests

Negative Binomial gives consistently the best fit for all degrees and for all three periods

Page 11: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Indegree QQ-plots – week 1

Page 12: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Outdegree QQ-plots – week 1

Page 13: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Degree QQ-plots – week 2

Page 14: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

DoC – statistical goodness-of-fit tests

Chi2-based and EDF-based tests

– Pearson chi2 statistic

– Kolmogorov - Smirnov test

Hypothesis for Geometric distribution rejected even at 1% level

Negative Binomial:

– the single distribution that passes the hypothesis testing at all significance levels (1%, 5%, 10%)

Inappropriateness of the power-law

Page 15: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Degree evolution with time (1)

How does evolution of infrastructure affect the degree of nodes?

Less clear answers…

Week Tracing Period Num Clients Total APs 1 17-24 October 2004 8880 459 2 2-9 March 2005 9049 532 3 13-20 April 2005 9881 574

Page 16: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Degree evolution with time (2)

Change of stochastic order after some degree value

Strong dependence on the location of new APs

– AP additions extending coverage contribute small DoCs

– APs in busier places contribute high degrees

Page 17: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Edge weights vs. distance (1)

similar approach : visual inspection and statistical analysis

Scatterplot for the three periods

• Negative correlation as expected

Page 18: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Edge weights vs. distance (2)

Negative correlation non-linear

Spearman rank correlation coefficient instead of the Pearson product-moment coefficient

Hypothesis of independence between the two is rejected at significance levels << 1%

chi2 test for independence over contingency table

chi2 statistic values = 4-7 times the critical values at the 1% statistical significance level

c1 c2 … cj … cp r1 r2 .. ri # of AP pairs with edge weight in the

jth bin and physical distance in the ith bin

… rr

Edge weights

Distance of edge APs

Page 19: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Graph demonstration – week 1

week 1 – Oct 2004

Page 20: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Graph demonstration – week 2

week 2 – Mar 2005

Page 21: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Graph demonstration –week 3

week 3 – Apr 2005

Page 22: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

Current work

Get graph “signature” for other infrastructures

– First target : Dartmouth wireless network

– First results show agreement in the graph degree distribution (Neg. Binomial)

Repeat analysis for smaller time-scales

– Down to 1 hour or 1-hour intervals over whole week

– More interesting for system engineering functions

– First results show less concise characterization – best-fit distributions vary with time

Page 23: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

UNC/FORTH Web Archive

Online archiving of datasets

– http://www.cs.unc.edu/Research/mobile/datatraces.htm

– Login/passwd access after free registration

Web repository of wireless measurement data

– Packet header traces, SNMP, SYSLOG, signal quality measurements

– Joint effort between Mobile Computing Groups in UNC & FORTH

– Complements similar efforts (e.g., CRAWDAD)

Page 24: M. Papadopouli 1,2,3, M. Moudatsos 1, M. Karaliopoulos 2 1 Institute of Computer Science, FORTH, Heraklion, Crete, Greece 2 University of North Carolina,

WiTMemo’06

Second International workshop on Wireless Traffic Measurements and Modeling

(WiTMeMo’06)

August 5th, 2006

Boston

http://www.witmemo.org