Post on 22-Dec-2015
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
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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