canqueue september 15, 20061 performance modeling of stochastic capacity networks carey williamson...

CanQueue September 15, 2006 1

Performance Modeling ofStochastic Capacity Networks

Carey Williamson iCORE Chair

Department of Computer ScienceUniversity of Calgary


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)


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


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


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]


Cellular Network Terminology

BSCPSDN

BS

Forward

Reverse

MS


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.


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)


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!)


“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


Soft Capacity: “Cell Breathing”

The effective service area expands and contracts according to the number of active users!


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)


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?


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


Circuit-Switched Network Model

Capacityfor C Calls


Markov Chain Model

.. .State0

State1

StateN

2 N

•Call arrival process: Poisson

•Call holding time distribution: Exponential

Blockingstate


Erlang B Results

2%


Erlang B Model Summary

CapacityC

OfferedLoad

BlockingProbability

p


Our Goal: Effective Capacity Model

EquivalentCapacity

OfferedLoad

BlockingProbability

p

DroppingProbability

d

DroppingPolicy


Modeling Methodology Overview

SimulationApproach

AnalyticApproach

SystemModel

CapacityModel

TrafficModel


Traffic Model

.. .State0

State1

StateN

.. .

2 N

•Arrival process: Poisson, Self-similar

•Holding time: Exponential, Pareto


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


Stochastic Capacity Example


Stochastic Capacity Terminology

“High variance”

“Low variance”



“High frequency”

“Low frequency”



“Correlated”

“Uncorrelated”


Stochastic Capacity Model

}{ ic

H

L

Highvalue

Lowvalue

Mediumvalue

...

},{ HHc

},{ MMc

},{ LLc

•Value process {Ci}

•Timing process {ti}

}{ i


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


Full Model Structure

CapacityVariation

Traffic Process

BlockingStates

DroppingTransitions


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


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


Effect of Capacity Value Mean

Large capacity C = 50 (60% load)

Medium capacity C = 40 (75% load)

Small capacity C = 30 (100% load)


Effect of Capacity Value Variance

Medium variance (75% load)

High variance (75% load)

Low variance (75% load)


Effect of Capacity Correlation

Uncorrelated

Correlated


Effect of Capacity Timing Process


Effect of Call Dropping Policy (1 of 2)


Effect of Call Dropping Policy (2 of 2)


Effect of Relative Time Scale

R = E[call arrivals/capacity change]


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


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!


Our Goal: Effective Capacity Model

EquivalentCapacity

OfferedLoad

BlockingProbability

p

DroppingProbability

d

DroppingPolicy


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.


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.


Thanks!

Questions? Credits:

Hongxia Sun Jingxiang Luo Qian Wu S. Dharmaraja

For more information: Email [email protected] http://www.cpsc.ucalgary.ca/~carey

canqueue september 15, 20061 performance modeling of stochastic capacity networks carey williamson...

Documents

jobs slide

soft handoff

simulation slide

neighbour cells handoff

handoff traffic

systems loss systems

possible computing nodes

reverse ms slide