ldu parametrized discrete-time multivariable mrac and application to a web cache system
DESCRIPTION
LDU Parametrized Discrete-Time Multivariable MRAC and Application to A Web Cache System. Ying Lu, Gang Tao and Tarek Abdelzaher University of Virginia. Outline. Web cache system modeling & identification MRAC based on LDU parametrization Implementation Evaluation. - PowerPoint PPT PresentationTRANSCRIPT
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LDU Parametrized Discrete-Time Multivariable MRAC
and Application to A Web Cache System
Ying Lu, Gang Tao and Tarek Abdelzaher
University of Virginia
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Outline
• Web cache system modeling & identification
• MRAC based on LDU parametrization
• Implementation
• Evaluation
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Examples of Control Theory Application in Computer Science
• Network flow control (TCP/IP - RED)– C. Hollot et al. (U.Mass, INFOCOM 2001)
• Admission control in computing system– J. Hellerstein et al. (IBM, IEEE ISINM 2001 )
• Apache server utilization control– T. F. Abdelzaher et al. (UVA, IEEE TPDS 2001)
• Apache QoS differentiation– C. Lu et al. (UVA, IEEE RTAS 2001)
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System Dynamics and Uncertainties
• Computer systems are dynamic– Current output depends on “system history”
– Queuing delays
• System model parameters are uncertain– software and hardware configuration changes
– workload changes
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Web Caching Architecture
H: hit rate, the rate at which valid requests can be satisfied without contacting the web server
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Differentiated Web Caching
• Requests are classified
• Different class has different level of service
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Caching Differentiation: A Feedback Control Problem
H1 : H2 : … : HN+1 = c1 : c2 : … : cN+1
Hi — average hit rate of classi, ci — QoS specification Si — disk space proportion of content classi
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System Identificationy(k) = Ay(k-1) + Bu(k-1)
y(k) = [y1(k), y2(k)]T
u(k) = [u1(k), u2(k)]T
A, B R2x2
apply a gradient algorithm to estimate the web cache system parameter matrix A & B
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Model Validation
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ImplementationService differentiation in Squid web cache• Timer: manage control loop execution frequency
• Output sensor– measure smoothed average hit rates– report the ratio of hit rates to controller
• Adaptive controller– execute the adaptive control algorithm– output the ratio of space proportions
• Actuator: manage the disk space allocation among classes
• Classifier: classify the requests
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Experimental Setup
• Testbed: – 8 AMD-based Linux machines
connected by 100-MHz Ethernet switch
• Clients: – 6 machines running Surge (a scalable
URL reference generator, a tool that generates realistic web workloads)
– 2 machines per content class
• Modified Squid web cache – cache size : files population = 1 : 33
• Apache web server
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Adaptive Controller Performance
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Conclusions• Web caching systems are dynamic
• System identification is feasible
• On line adaptation is desirable
• An LDU parametrized MRAC is derived for MIMO systems
• MRAC is applied to a web caching system
• Adaptive control is implemented on Squid web cache
• Proportional hit rate differentiation service is achievable despite system uncertainties