By Y.C. Tay
This publication is an advent to analytical functionality modeling for desktops, 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 guide for changing into knowledgeable functionality analyst. fairly, the target is to aid the reader build uncomplicated types for reading and realizing the structures within which they're . Describing a classy process abstractly with mathematical equations calls for a cautious selection of assumptions and approximations. those assumptions and approximations make the version tractable, yet they have to now not get rid of crucial features of the approach, nor introduce spurious homes. to assist the reader comprehend the alternatives and their implications, this e-book discusses the analytical types in 20 learn papers. those papers conceal a large diversity of subject matters: processors and disks, databases and multimedia, worms and instant, and so on. An Appendix offers a few questions for readers to workout their figuring out of the types in those papers. desk of Contents: Preliminaries / strategies and Little's legislation / unmarried Queues / Open platforms / Markov Chains / Closed structures / Bottlenecks and movement Equivalence / Deterministic Approximations / brief research / Experimental Validation and research / research with an Analytical version
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Extra info for Analytical Performance Modeling for Computer Systems
I Note that the approximation Vi ≈ λrequest in Sec. 3 would not work well in Sec. 4, where requests can be dropped by the concurrency limit. NetworkProcessor  This paper gives an example of how an analytical model can be used to explore a design space, namely the implementation of some software. Specifically, they consider the implementation of a network application on a given network processor. 4. , cycles, threads, memory) at the packet processors. An implementation decides its data flow through the components, and thus its performance.
Suppose queue i has Ki servers, with average service time Si per job. Let Vi be the average number of visits to queue i per job, and service demand Di = Vi Si . By Little’s Law, the utilization per server is XDi Vi XSi = ≤ 1, Ki Ki so X ≤ Ki . Di This is true for every i, so X ≤ min i Ki . Di A queue that gives the minimum Ki /Di or (equivalently) the maximum service demand per server Di /Ki is called a bottleneck. A bottleneck also maximizes XDi /Ki , so it has highest utilization per server. There is always a maximum Di /Ki , so a bottleneck always exists.
Here, the existence of a steady state for λ = μ illustrates the impact of determinism in arrival times. 4 DISCUSSION We continue the discussion of StreamJoins  and introduce SleepingDisks  and StorageAvailability . StreamJoins  For limited compute power (Sec. 1), the streams are sampled, resulting in effective arrival rates of λa and λb . 16 says that the sampled streams are also Poisson. However, it appears from λa + λb = μ in Eq. (13) that the authors assume the stream arrivals and service times are deterministic; otherwise, the average number of tuples in memory can grow without bound, like in Fig.