Abstract

Clusters of Web caches are extensively used by different types of organizations, including companies, universities, ISPs, and CDNs. To model Web caches, we must account for two types of stochastic events: objects being pulled into/out of the cache cluster at random times, and caches going up and down at random times. Detailed stochastic models of such complex systems quickly become intractable. In this paper we propose a stochastic fluid model which captures the salient characteristics of a cache cluster. The stochastic fluid model replaces the object arrivals to the cluster and departures (object modification/expiration) with a fluid flow, but maintains the up/down dynamics of the original system. The model can be applied to a variety of cluster routing policies, and provides a simple means to estimate the hit rate. We compare the results of the stochastic fluid model with that of a simulation of the real system. We find the fluid model to not only be a close approximation, but also to exhibit the key qualitative properties of the original system. We conclude that stochastic fluid models show great potential in modeling a variety of content distribution systems.

Author Keywords: Web caching; Fluid models; Stochastic processes; Palm calculus

Article Outline

1. Introduction

2. Overview of cache clusters

3. A model for cache clusters

3.1. Dynamic microscopic model

3.2. Stochastic fluid model

4. Hit rate analysis

4.1. Infinite storage capacity

4.2. Finite storage capacity

5. Performance of the caching system

5.1. Qualitative behavior

5.2. Comparison of partition hashing and winning hashing

6. Numerical results

6.1. Unlimited capacity

6.2. Validation for finite storage

7. Concluding remarks

Appendix A. Stationary distribution of the Engset model at jump times

Appendix B. Uniqueness of the solution of (12)

References

Vitae

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