Fig. 1. Conceptual illustration of Web cache filtering effect.

Fig. 2. Time series plot of request arrival process for empirical Web proxy workload: (a) interval size: 1 s; (b) interval size: 1 h.

Fig. 3. Evidence of self-similar request arrival process for empirical Web proxy workload: (a) time series plot; (b) autocorrelation function; (c) variance–time plot; (d) R/S Pox plot.

Fig. 4. Characteristics of the request arrival process for empirical Web proxy workload: (a) PDF; (b) CDF; (c) LLCD.

Fig. 5. Illustration of the proxy cache filter effects on the empirical Web proxy workload: (a) full trace time series (interval: 30 min); (b) busy period time series (interval: 5 min); (c) full trace hit ratio (interval: 30 min); (d) busy period hit ratio (interval: 5 min).

Fig. 6. Evidence of self-similar request arrival process for filtered Web proxy workload: (a) time series plot; (b) autocorrelation function; (c) variance–time plot; (d) R/S Pox plot.

Fig. 7. Characteristics of the filtered arrival process as a function of cache size (empirical workload, LFU policy): (a) PDF; (b) CDF; (c) LLCD.

Fig. 8. Characteristics of the filtered arrival process as a function of cache replacement policy (empirical workload, 8MB cache).

Fig. 9. Characteristics of the filtered arrival process as a function of cache size (H = 0.75, LFU policy).

Fig. 10. Gamma probability density function.

Fig. 11. Gamma distribution model for input request arrival count distribution (empirical workload, γ = 2.67, β = 7.60).

Fig. 12. Gamma distribution model for filtered request arrival count distribution (empirical workload, γ = 1.63, β = 7.22).

Fig. 13. Gamma distribution models for filtered request arrival count distribution (synthetic workload: 20 requests/s, H = 0.75, Z = 0.80, LFU cache, Gamma model (γ, β, μ).

Fig. 14. Example of a two-level Web proxy caching hierarchy.

Fig. 15. Synthetic self-similar workload traces used in simulations: (a) trace 1: H = 0.70, Z = 0.75; (b) trace 2: H = 0.80, Z = 0.80.

Fig. 16. Time series plots of request arrival processes for filtered workloads λ^′₁ and λ^′₂: (a) λ^′₁: interval size = 1 s; (b) λ^′₁: interval size = l h; (c) λ^′₂: interval size = 1 s; (d) λ^′₂: interval size = l h.

Fig. 17. Characteristics of filtered workload λ^′₁: (a) PDF; (b) CDF; (c) LLCD.

Fig. 18. Evidence of self-similarity in filtered workload λ^′₁: (a) autocorrelation function; (b) variance–time plot; (c) R/S Pox plot.

Fig. 19. Characteristics of aggregate request arrival process λ₃: (a) PDF; (b) CDF; (c) LLCD.

Fig. 20. Evidence of self-similar for aggregate request arrival process λ₃: H ≈ 0.76: (a) time series; (b) autocorrelation function; (c) variance–time plot; (d) R/S Pox plot.

Fig. 21. PDF for filtered workloads λ^′₁ and λ^′₂.

Fig. 22. Modeling of aggregate workload λ₃: (a) PDF; (b) CDF; (c) LLCD.

Characteristics of empirical Web proxy workload (U of S proxy)

Experimental factors and levels for studying cache filter effects

Simulation results for different cache sizes (empirical workload, LFU policy)

Simulation results for different cache replacement policies (empirical workload, 8MB cache)

Characteristics of synthetic Web proxy workloads

Simulation results for different cache sizes (synthetic workload, H = 0.9, Z = 0.8, LFU policy)

Simulation results for different replacement policies (synthetic workload, H = 0.9, Z = 0.8, 8MB cache)