By Y.C. Tay

This ebook is an advent to analytical functionality modeling for desktops, i.e., writing equations to explain their functionality habit. it truly is available to readers who've taken college-level classes in calculus and likelihood, networking, and working structures. this isn't a coaching handbook for changing into knowledgeable functionality analyst. quite, the target is to aid the reader build uncomplicated types for studying and realizing the structures within 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 procedure, nor introduce spurious houses. to assist the reader comprehend the alternatives and their implications, this publication discusses the analytical versions in 20 learn papers. those papers disguise a extensive diversity 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 knowing of the types in those papers. desk of Contents: Preliminaries / ideas and Little's legislation / unmarried Queues / Open structures / Markov Chains / Closed platforms / Bottlenecks and stream Equivalence / Deterministic Approximations / temporary research / Experimental Validation and research / research with an Analytical version

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4, we get corresponding bounds on response time R from R = T − Z. 2. 2: For a closed network, the shapes of throughput X and system time T for large N are determined by bottlenecks [22]. 2 FLOW EQUIVALENCE Recall that, for an M/M/3 queue, the service rate depends on the number of jobs k in the queue. 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.

5)). Like GPRS [23], the model is a discrete-time Markov chain with transition probabilities between states (instead of transition rates in the case of continuous-time Markov chains). 35 CHAPTER 5 Closed Systems As we can see from the previous chapter, the solution of closed queueing networks can be very tedious. This is so even for separable networks (which are easy to solve if they are open, as we saw in Chapter 3). The solution is easier if we give up state probabilities, and only solve for average values.

Similarly, if the computing resources are also limited (Sec. 3), then the sampled streams may not have the intended λa and λb . SleepingDisks [37] 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.