By Y.C. Tay
This publication is an advent to analytical functionality modeling for computers, i.e., writing equations to explain their functionality habit. it really is available to readers who've taken college-level classes in calculus and chance, networking, and working platforms. this isn't a coaching handbook for changing into a professional functionality analyst. quite, the target is to assist the reader build easy versions for examining and knowing the platforms during which they're . Describing a classy approach abstractly with mathematical equations calls for a cautious selection of assumptions and approximations. those assumptions and approximations make the version tractable, yet they need to no longer eliminate crucial features of the process, nor introduce spurious houses. to aid the reader comprehend the alternatives and their implications, this publication discusses the analytical types in 20 learn papers. those papers conceal a large variety of subject matters: processors and disks, databases and multimedia, worms and instant, and so forth. An Appendix presents a few questions for readers to workout their figuring out of the versions in those papers. desk of Contents: Preliminaries / thoughts and Little's legislation / unmarried Queues / Open platforms / Markov Chains / Closed structures / Bottlenecks and circulation Equivalence / Deterministic Approximations / brief research / Experimental Validation and research / research with an Analytical version
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Then |ρXY | ≤ 1. It follows that |EXY − μX μY | ≤ √ (V arX)(V arY ), so EXY ≈ μX μY if V arX is small. To give another example, although E( X Y) = E X Y ≈E X EY = EX EY 1 EX, EY in general, AVA gives since 1 is a constant. EY 50 7. DETERMINISTIC APPROXIMATIONS AVA is a simplistic approximation that is widely used in analytical modeling (including those surveyed in this book). 2 FLUID APPROXIMATION Although jobs are discrete, treating their movement as a continuous fluid flow can significantly simplify the analysis without losing important details.
3). The real use of flow equivalence is for nonseparable networks (as when the load-dependent queue models, say, a cache hierarchy or a wireless cell), for which it is an approximate technique. This approximation is good if the subnetwork reaches steady state faster than the complementary network . Intuitively, every arrival to the subnetwork sees it in equilibrium with a steady K value. 3 EQUIVALENCE BETWEEN OPEN AND CLOSED If a closed system is easier to analyze (because population size is fixed, say), one can approximate an open system by flow equivalence with a closed system, as illustrated in Fig.
Similarly, if the computing resources are also limited (Sec. 3), then the sampled streams may not have the intended λa and λb . SleepingDisks  Fig. 6 shows the system for this paper. The input parameters include arrival rate αi , service time as specified by Exp(tij ) and V ar(tij ), transition time Ti , power Pij , Pij , and Pij . The main performance measures are response time (Fig. 7), transaction rate (Fig. 12a) and energy per transaction (Fig. 12b). 4. DISCUSSION 19 The main issues are: (i) the tradeoff between performance and energy and (ii) adaptive disk layout in response to dynamic workload changes.
Analytical Performance Modeling for Computer Systems by Y.C. Tay