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
Outline
Background

Motivation
Wireless infrastructure
Measurement data
Describing wireless network access with
graphs
–
Graph definition/generation
–
Graph properties
Current work
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
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
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
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)
SYSLOG message generation
UNC Wired
Network
Wireless
Network
Router
Internet
User i
AP 1
AP 2
User D
AP3
Switch
:
SYSLOG message(s)
User j
1
time
t
1
User j association
2
time
t
2
Roaming to AP2
disconnection
time
t
4
4
time
t
3
Roaming to AP3
3
Roaming activity as a graph
AP i
湯摥 椠
嘠
Client transition between APs
†
敤来
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, G
Τ
= (
V
T
, E
T
)
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)
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
DoC
–
visual goodness

of

fit tests
Several discrete distributions tested
–
Negative Binomial
–
Geometric
–
Binomial
–
Poisson
ML estimation of parameters for the statistical
tests
乥N慴楶i⁂楮潭楡i 杩癥猠捯湳n獴敮瑬礠瑨攠扥獴s晩琠
for all degrees and for all three periods
Indegree QQ

plots
–
week 1
Outdegree QQ

plots
–
week 1
Degree QQ

plots
–
week 2
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
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 200
4
8880
459
2
2

9 March 2005
9049
532
3
13

20 April 2005
9881
574
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
Edge weights vs. distance (1)
similar approach : visual inspection and
statistical analysis
Scatterplot for
the three periods
•
Negative correlation as expected
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
c
1
c
2
…
c
j
…
c
p
r
1
r
2
..
r
i
# of AP
pair
s with
edge weight
in the
j
th
bin and physical distance in the i
th
bin
…
r
r
Edge weights
Distance of
edge APs
Graph demonstration
–
week 1
week 1
–
Oct 2004
Graph demonstration
–
week 2
week 2
–
Mar 2005
Graph demonstration
–
week 3
week 3
–
Apr 2005
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
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)
WiTMemo
’
06
Second International workshop on Wireless
Traffic Measurements and Modeling
(WiTMeMo’06)
August 5
th
, 2006
Boston
http://www.witmemo.org
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