Yung-Chih ChenJim Kurose and Don Towsley

Computer Science DepartmentUniversity of Massachusetts Amherst

A Mixed Queueing Network Model of Mobility in a Campus Wireless

Network

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Motivation

• Mobility modeling (till now)– Theoretical models• Random WayPoint/Walk

– Real world user mobility modeling• Mobility pattern [Kim’07, Hsu’06]

– Contact-based mobility [Chaintreau’06, Hsu’10]

– Group-based mobility [Hong’99, Wang’02, Chen’10]

• Merge/split process [Heimlicher’10]

• Modeling becomes complicated….

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• Simple model to capture user behavior– Users moving from AP to AP – Predict system level performance

• AP occupancy distribution

– Predict user level performance• Time stay in network • Number of visited APs

• Network dimensioning

Goal

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User Behavior: Campus Network

• Focus on modeling the period when• network more active and heavily used

• A closer look of this stable period

MidnightEarly Morning

Evening

User Behavior: Campus Network

StayTransition

Depart

APi

APj

• Some “arrive and depart” • Some “always” in the network• Transitions between APs • Stay times at AP

APM

5

Arrive

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Model• A mixed network consists of two types of users

• Open class (, , )– Arrive, stay, and eventually leave

• Poisson arrivals, general stay time

– APs are modeled as M/G/∞ queues• As if infinite number of servers

– AP Occupancy Distribution • Poisson distribution

– AP load (open):

• Closed class (N, )– Always active in the network

• N : fixed population (average over each day)• : Visit ratio to AP

– AP occupancy distribution • Binomial distribution:

Poisson distribution – AP load (closed):

• Mixed Network – APs are modeled as M/G/∞ queues– AP occupancy distribution

• Open PDF + closed PDF: Poisson distribution • APi load:

APi

APj

APk

𝜆𝑖

𝑝𝑖𝑗

𝑝𝑘0stay:

APi APj

APk

M/G/∞ queues

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Trace • Mobility – User moving from AP to AP– User/AP association/disassociation messages

• Dartmouth Trace* – 17 weeks on Dartmouth College campus

• 6000+ users• 550+ Cisco APs

– Simple Network Management Protocol (SNMP)• Central controller polls each AP every 5 minutes • AP replies which clients (MAC addresses) are with it

– Know when a user joins network, how long he stays – Infer departure by a user’s absence in the subsequent poll*CRAWDAD archive:

http://www.crawdad.org/

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Trace (Con’t)• Interested in periods most active– Remove weekends/holidays/inter-session breaks– Stable network traffic

• 9 AM to 5 PM• 544 APs with 5,715 distinct MAC addresses

Validation: User Occupancy at APs

Example: The most heavily loaded AP

How about other APs?

• Kolmogorov-Smirnov goodness of fit (K-S)

• : CDF of empirical data • : CDF of model predictions• : K-S statistic (max diff. of 2 dist.)

• Accept if small enough ( 95% conf. level)

APi load: (parameters obtained from the trace)

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• : network stay time starting at APi

• Can be solved analytically

• Mean network stay time: –Model prediction : 141 mins – Empirical average: 133 mins

• # visited APs: let =1–Model prediction : 2.1 APs – Empirical average: 2.07 APs

Validation: Mean Network Stay Time, #Visited APs

Only 5% difference !

Only 1.4% difference !

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Network Dimensioning

• What if arrival rate/population increase? – Assume user mobility does not change

• : open class user’s average stay time at APi

• : closed class user’s fraction of time visiting APi

– Assume AP has capacity K• Serve K users simultaneously w/ guaranteed QoS• APi is overloaded if

– AP can not meet all users’ QoS– =1% in the following scenarios

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• Increase of arrivals to each AP (arrival rate )

Network Dimensioning -Open

=1=2=3=4=5

Must triple capacity if 5 to maintain the same QoS

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• Increase of closed population (N )

Network Dimensioning - Closed

=441=882=1323=1764=2205

Must double capacity if N 5N to maintain the same QoS

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Conclusion• Proposed simple queueing model of mobility

– open and closed class users

• Validated against empirical traces

• Good predictions of metrics of interest – System-level

• 93.25 % accuracy on user occupancy distribution

– User-level • Mean network stay time: 8 minutes difference • # visited APs: 1.4% difference

• The model can be used for network dimensioning– Increase of arrival rate to each AP – Increase of always active population

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References• W.-j. Hsu, D. Dutta, and A. Helmy. ”Mining behavioral groups in large wireless lans,”

Mobicom’07• M. Kim and D. Kotz. “Extracting a mobility model from real user traces,” Infocom’06 • A. Chaintreau, P. Hui, J. Crowcroft, C. Diot, R. Gass, and J. Scott. “Impact of human

mobility on the design of opportunistic forwarding algorithms,” Infocom’06• W.-j. Hsu and A. Helmy. “On nodal encounter patterns in wireless lan traces,” IEEE

Transactions on Mobile Computing’10• S. Heimlicher and K. Salamatian. “Globs in the primordial soup: the emergence of

connected crowds in mobile wireless networks” MobiHoc’10.• Y.-C. Chen, E. Rosensweig, J. Kurose, and D. Towsley. “Group detection in mobility

traces,” IWCMC’10 • X. Hong, M. Gerla, G. Pei, C-C. Chiang. “A Group Mobility Model for Ad Hoc Wireless

Networks,” IEEE MSWiM’99• K. H. Wang, and B. Li. “Group Mobility and Partition Prediction in Wireless Ad-Hoc

Networks,” ICC’02

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Thanks!

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• Departure threshold – User did leave the system and returned – User was in motion, moving from AP1 to AP2 – Missing SNMP reports

Trace Pre-Processing (Con’t)

Session: start w/ first AP association; end w/ disassociating w/ all campus APs

S1 S2

∆

S’=S1+ ∆ +S2

<threshold

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• Multiple associations– In the same 5-minute window, more than 1 AP report a

specific user is associated with it– User is in motion, moving from 1 AP to another AP(s) – Keep the last associated AP, and remove all the rest

• Ping-Pong effect – User associates with a fixed set of AP, one after one

but only with very short amount of time – Mainly due to weak Wi-Fi signal – Hard to tell when this happens/ how many APs involved– Treat as regular transitions

Trace Pre-Processing (Con’t)

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Verifying Poisson Assumption

• Poisson arrivals to each AP – Aggregation of Poisson processes is Poisson– Daily inter-arrival times to campus network

• Average (exponential distribution)– : squared correlation from 0~1 (1 as perfect fit)

• Explain 96% of variability

– Tail outliers• 0.23%• Improve

– 0.02 on average

worst fitted day (

User Occupancy at APs

• Open class PDF– Poisson distribution

• AP load (open):

• Closed class PDF – Binomial distribution: Poisson distribution

• AP load (closed):

• Mixed network PDF– Open PDF + closed PDF

• Poisson distribution

– APi load: 20