CanQueue September 15, 20061 Performance Modeling of Stochastic Capacity Networks Carey Williamson...
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CanQueue September 15, 2006 1
Performance Modeling ofStochastic Capacity Networks
Carey Williamson iCORE Chair
Department of Computer ScienceUniversity of Calgary
CanQueue September 15, 2006 2
Introduction
There exist many practical systems in which the system capacity varies unpredictably with time
These systems are complicated to model and understand
Main focus of this talk: Stochastic capacity networks Lots of modeling issues and questions A few answers (mostly from simulation)
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Some Examples
Safeway checkout line Variable-rate servers Load-dependent servers Grid computing center Priority-based reservation networks Wireless Local Area Networks (WLANs) Wireless media streaming scenarios Handoffs in mobile cellular networks “Soft capacity” cellular networks
Queueingsystems
Losssystems
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Some Examples
Safeway checkout line Variable-rate servers Load-dependent servers Grid computing center Priority-based reservation networks Wireless Local Area Networks (WLANs) Wireless media streaming scenarios Handoffs in mobile cellular networks “Soft capacity” cellular networks
Queueingsystems
Losssystems
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Grid Computing Example
Jobs of random sizes arrive at random times to central dispatcher, and are then sent to one of M possible computing nodes
If a computing node fails, then all jobs that are currently in progress on that node are irretrievably lost
Performance impacts: Lost work needs to be redone Increased queue delay for waiting jobs
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Wireless LAN (WLAN) Example
An IEEE 802.11b WLAN (“WiFi”) supports four different physical transmission rates: 1 Mbps, 2 Mbps, 5.5 Mbps, 11 Mbps
Stations can dynamically switch between these rates on a per-frame basis depending on signal strength and perceived channel error rate
Performance impacts: The presence of one low-rate station actually
degrades throughput for all WLAN users [Pilosof et al. IEEE INFOCOM 2003]
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Cellular Handoff Example Mobile phones communicate via a
cellular base station (BS) Movement of active users beyond
the coverage area of current BS necessitates handoff to another BS
If no resources available, drop call Possible strategies:
Guard channels (static or dynamic) Power control, “soft handoff”, etc.
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Handoff Traffic in a Base Station
Cell Site
New Calls(Poisson)
Channel Pool with total C channels
Call completion (exponentialdistribution)
Handoff Calls
To neighbour cells
Handoff Calls(non-Poisson)
From neighbour cells
g
Guard channels (static scheme)
[Dharmaraja et al. 2003]
C-g(blocking possible)
(dropping possible)
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Handoff Traffic in a Base Station
Cell Site
New Calls(Poisson)
Channel Pool with total C channels
Call completion (exponentialdistribution)
Handoff Calls
To neighbour cells
Handoff Calls(non-Poisson)
From neighbour cells
g
Guard channels (dynamic scheme)
C-g(blocking possible)
(dropping possible)
(dropping possible!)
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“Soft Capacity” Example
Problem originally motivated by research project with TELUS Mobility
Q: How many users at a time can be supported by one BS? - CLW
A: “It depends” - MW CDMA cellular systems are typically
interference-limited rather than channel limited (i.e., time varying)
Intra-cell and inter-cell interference
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Soft Capacity: “Cell Breathing”
The effective service area expands and contracts according to the number of active users!
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Observation and Motivation
Networks with time-varying capacity tend to exhibit higher call blocking rates and higher outage (dropping) probabilities than regular networks
Investigating performance in such systems requires consideration of the traffic process as well as the capacity variation process (and interactions between these two processes)
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Research Questions
What are the performance characteristics observed in stochastic capacity networks?
How sensitive are the results to the parameters of the stochastic capacity variation process?
Can one develop an “effective capacity” model for such networks?
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Background: Erlang Blocking Formula
The Erlang B formula expresses the relationship between call blocking, offered load, and the number of channels in a circuit-based network
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Markov Chain Model
.. .State0
State1
StateN
2 N
•Call arrival process: Poisson
•Call holding time distribution: Exponential
Blockingstate
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Our Goal: Effective Capacity Model
EquivalentCapacity
OfferedLoad
BlockingProbability
p
DroppingProbability
d
DroppingPolicy
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Modeling Methodology Overview
SimulationApproach
AnalyticApproach
SystemModel
CapacityModel
TrafficModel
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Traffic Model
.. .State0
State1
StateN
.. .
2 N
•Arrival process: Poisson, Self-similar
•Holding time: Exponential, Pareto
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Traffic and Capacity Example
Traffic Arrival and Departure Process (Point Process) t
Fixed Capacity C = 10
Fixed Capacity C = 4Fixed Capacity C = 5
TrafficOccupancyProcess(CountingProcess)
Stochastic Capacity
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Stochastic Capacity Model
}{ ic
H
L
Highvalue
Lowvalue
Mediumvalue
...
},{ HHc
},{ MMc
},{ LLc
•Value process {Ci}
•Timing process {ti}
}{ i
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Effective Capacity
.. .State0
State1
StateN
.. .
2 N
H
L
Highvalue
Lowvalue
Mediumvalue...
+
•Effects of Capacity Value process
•Effects of Capacity Timing process
•Effect of Correlations
•Interactions between Traffic and Capacity
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Full Model Structure
CapacityVariation
Traffic Process
BlockingStates
DroppingTransitions
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Parameters in Simulations
Parameter Level
NetworkTraffic
Call arrival rate (per sec) 1.0
Mean holding time (sec) 30
NetworkCapacity
(calls)
Mean 30, 40, 50
Standard Deviation 2, 5, 10
Mean Time Between Capacity Changes (sec)
10, 15, 30, 60, 120
Hurst Parameter H (for LRD model) 0.5, 0.7, 0.9
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Results and Observations (Preview)
Factors that matter: Mean of capacity value process Variance of capacity value process Correlation of capacity value process Frequency of capacity timing process Choice of call dropping policy used Relative time scales of joint processes
Factors that don’t matter: Distribution for capacity timing process
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Effect of Capacity Value Mean
Large capacity C = 50 (60% load)
Medium capacity C = 40 (75% load)
Small capacity C = 30 (100% load)
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Effect of Capacity Value Variance
Medium variance (75% load)
High variance (75% load)
Low variance (75% load)
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Results and Observations (Recap)
Factors that matter: Mean of capacity value process Variance of capacity value process Correlation of capacity value process Frequency of capacity timing process Choice of call dropping policy used Relative time scales of joint processes
Factors that don’t matter: Distribution for capacity timing process
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Summary and Conclusion
Studied call-level performance in a network with stochastic capacity variation
Shows influences from the properties of the stochastic capacity variation process
Shows that mean and variance of capacity process have the largest impact, as do the correlation structure and timing
Shows impact of interactions between traffic and capacity processes
One step closer to our goal, but the hard part is still ahead!
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Our Goal: Effective Capacity Model
EquivalentCapacity
OfferedLoad
BlockingProbability
p
DroppingProbability
d
DroppingPolicy
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References
H. Sun and C. Williamson, “Simulation Evaluation of Call Dropping Policies for Stochastic Capacity Networks”, Proceedings of SCS SPECTS 2005, Philadelphia, PA, pp. 327-336, July 2005.
H. Sun and C. Williamson, “On Effective Capacity in Time-Varying Wireless Networks”, Proceedings of SCS SPECTS 2006, Calgary, AB, July 2006.
H. Sun, Q. Wu, and C. Williamson, “Impact of Stochastic Traffic Characteristics on Effective Capacity in CDMA Networks”, to appear, Proceedings of P2MNet, Tampa, FL, Nov. 2006.
H. Sun and C. Williamson, “On the Role of Call Dropping Controls in Stochastic Capacity Networks”, submitted for publication, 2006.
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Related Work
S. Dharmaraja, K. Trivedi, and D. Logothetis, “Performance Modelling of Wireless Networks with Generally Distributed Hand-off Interarrival Times”, Computer Communications, Vol. 26, No. 15, pp. 1747-1755, 2003.
V. Gupta, M. Harchol-Balter, A. Scheller-Wolf, and U. Yechiali, “Fundamental Characteristics of Queues with Fluctuating Load”, Proceedings of ACM SIGMETRICS 2006, St. Malo, France, June 2006.
G. Haring, R. Marie, R. Puigjaner, and K. Trivedi, “Loss Formulae and Optimization for Cellular Networks”, IEEE Transactions on Vehicular Technology, Vol. 50, No. 3, pp. 664-673, 2001.
B. Haverkort, R. Marie, R. Gerardo, and K. Trivedi, Performability Modeling: Techniques and Tools, 2001.
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Thanks!
Questions? Credits:
Hongxia Sun Jingxiang Luo Qian Wu S. Dharmaraja
For more information: Email [email protected] http://www.cpsc.ucalgary.ca/~carey