Hierarchical Reuse Model 3 1 Figure 1.17. TSO storage pools: distribution of track interarrival times. Figure 1.18. TSO storage pools: distribution of record interarrival times. 32 THE FRACTAL STRUCTURE OF DATA REFERENCE Figure 1.19. OS/390 system storage pools: distribution of track interarrival times. Figure 1.20. OS/390 system storage pools: distribution of record interarrival times. Hierarchical Reuse Model 33 single - reference residency time lengthens. Thus, as we should expect, these plots suggest an important role for processor file buffers in the production database storage pools. In Chapters 3 and 5, we shall sometimes adopt a mathematical model in which multiple workloads share the same cache or processor buffer area, and each individual workload conforms to the hierarchical reuse model. This results in a series of equations of the form (1.5), one for each workload. In graphical terms, it corresponds to fitting each workload’s plot of interarrival statistics with a straight line. Collectively, Figures 1.2, 1.3, and 1.1 1 through 1.20 provide the justification for adopting the mathematical model just described. The multiple workload hierarchical reuse model, as just outlined in the previous paragraph, is both sufficiently simple, and sufficiently realistic, to provide a practical framework for examining how to get the most out of a cache shared by multiple, distinct workloads. 34 THE FRACTAL STRUCTURE OF DATA REFERENCE Notes 1 Assumes a track belonging to the 3380 family of storage devices. 2 Assumes a track belonging to the 3390 family of storage devices. Chapter 2 HIERARCHICAL REUSE DAEMON To conduct realistic performance benchmarks of storage subsystem perfor - mance, one attractive approach is to construct the required benchmark driver out of building blocks that resemble, as closely as possible, actual applications or users running in a realistic environment. This chapter develops a simple “toy” version of an application whose pattern of reference conforms to the hierarchical reuse model. Such a toy application can be implemented as an independently executing “daemon” [19], and provides a natural building block for I/O performance testing. In addition, it helps bring to life, in the form of a concrete example, the hierarchical reuse model itself. It is reasonably simple to implement a toy application of the form that we shall present, and to test its cache behavior directly against the characteristics of the hierarchical reuse model. Nevertheless, this chapter also provides a crude, asymptotic analysis to explain why we should expect the comparison to be a favorable one. To accomplish the needed analysis, we must first put the behavior of the hierarchical reuse model into a form convenient for comparison against the proposed toy application. With this background in place, we then propose, and analyze, a method by which it is possible to match this behavior synthetically. Finally, we illustrate the actual behavior of the proposed synthetic requests through simulation. 1. DESIRED BEHAVIOR Assuming that a pattern of requests obeys the hierarchical reuse model, consider the expected arrival rate λ(t), to a specific track, after an amount of time t has passed since some given I/O request. The behavior of λ(t) provides an alternative method of characterizing the hierarchical reuse model, which . workloads. 34 THE FRACTAL STRUCTURE OF DATA REFERENCE Notes 1 Assumes a track belonging to the 3380 family of storage devices. 2 Assumes a track belonging to the 3390 family of storage devices storage pools: distribution of track interarrival times. Figure 1.18. TSO storage pools: distribution of record interarrival times. 32 THE FRACTAL STRUCTURE OF DATA REFERENCE Figure 1.19 background in place, we then propose, and analyze, a method by which it is possible to match this behavior synthetically. Finally, we illustrate the actual behavior of the proposed synthetic requests