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LDU Parametrized Discrete-Time Multivariable MRAC and Application to A Web Cache System

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.

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LDU Parametrized Discrete-Time Multivariable MRAC and Application to A Web Cache System

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  1. LDU Parametrized Discrete-Time Multivariable MRAC and Application to A Web Cache System Ying Lu, Gang Tao and Tarek Abdelzaher University of Virginia

  2. Outline • Web cache system modeling & identification • MRAC based on LDU parametrization • Implementation • Evaluation

  3. 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) Examples of Control Theory Application in Computer Science

  4. 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

  5. Web Caching Architecture H: hit rate, the rate at which valid requests can be satisfied without contacting the web server

  6. Differentiated Web Caching • Requests are classified • Different class has different level of service

  7. 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

  8. System Identification • y(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

  9. Model Validation

  10. Implementation Service 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

  11. 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

  12. Adaptive Controller Performance

  13. 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

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