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 k – 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 iAP 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  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, G Τ = (V T, E T ) In the paper, T = 1 week – 3 different weeks are studied : Oct 04, 2-9 Mar 05, 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 Negative Binomial gives consistently the best fit 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…

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 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 – – 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