By Y.C. Tay
This e-book is an creation to analytical functionality modeling for computers, i.e., writing equations to explain their functionality habit. it's obtainable to readers who've taken college-level classes in calculus and chance, networking and working structures. this isn't a coaching handbook for turning into knowledgeable functionality analyst. quite, the target is to assist the reader build easy versions for examining and knowing the structures that they're in.
Describing a sophisticated method abstractly with mathematical equations calls for a cautious number of assumptions and approximations. They make the version tractable, yet they need to no longer eliminate crucial features of the method, nor introduce spurious properties.
To support the reader comprehend the alternatives and their implications, this ebook discusses the analytical types for 30 learn papers. those papers conceal a extensive variety of subject matters: processors and disks, routers and crawling, databases and multimedia, worms and instant, multicore and cloud, and so forth. An appendix offers many questions for readers to workout their realizing of the versions in those papers.
Table of Contents: Preface / Preliminaries / ideas and Little's legislation / unmarried Queues / Open structures / Markov Chains / Closed platforms / Bottlenecks and movement Equivalence / Deterministic Approximations / temporary research / Experimental Validation and research / research with an Analytical version / Bibliography / Author's Biography
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Additional resources for Analytical Performance Modeling for Computer Systems: Second Edition (Synthesis Lectures on Computer Science)
This is an example of a load-dependent queue, represented as with output rates X(1) = μ, X(2) = 2μ and X(k) = 3μ for k ≥ 3. We saw in Chapter 4 the computational tedium in solving a multi-dimensional Markov chain, and the idea of deriving a faster approximation through state aggregation. , aggregation of the subsystem), then solve the aggregated system (via flow equivalence). 3: Aggregating a subnetwork in Fig. 1 into a load-dependent queue. For example, the three-queue closed network in Fig. 1 can be decomposed by aggregating queues B and C into one load-dependent queue that represents a subnetwork, like in Fig.
An implementation decides its data flow through the components, and thus its performance. An analytical model facilitates a comparison of implementation possibilities, thus reducing implementation effort. IV does not illustrate the use of the model to compare different implementation possibilities. Fig. 1 shows the architecture of the network processor but, since the issue is resource management at the packet processors, the analytical model in Fig. 2 focuses on the packet processors and memory.
1 1 = , μ 1−ρ μ 36 5. CLOSED SYSTEMS Example: M/D/1 For M/D/1, although the average queue length seen by the Poisson arrivals is again the time average n, we no longer have W = n μ1 . This is because the deterministic service time is not memoryless, so the residual life of the job in service when a job arrives is no longer Little’s Law and Eq. 2 1 μ so W = = 1 μ . To confirm, n 1 ρ 1 1 1 ρ 1 − = 1− − = , λ μ 2 1−ρ μ μ 2(1 − ρ) μ (2−ρ)ρ 1 2(1−ρ) μ . ARRIVAL THEOREM Separability has been extended to closed networks.