By Y.C. Tay
This publication is an creation 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 likelihood, networking, and working structures. this isn't a coaching handbook for turning into a professional functionality analyst. quite, the target is to assist the reader build easy types for studying and figuring out the structures within which they're . Describing a sophisticated procedure abstractly with mathematical equations calls for a cautious number of assumptions and approximations. those assumptions and approximations make the version tractable, yet they need to now not eliminate crucial features of the approach, nor introduce spurious houses. to assist the reader comprehend the alternatives and their implications, this e-book discusses the analytical types in 20 examine papers. those papers hide a extensive diversity of issues: 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 versions in those papers. desk of Contents: Preliminaries / thoughts and Little's legislation / unmarried Queues / Open platforms / Markov Chains / Closed platforms / Bottlenecks and circulate 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
The author adopts an open model by fixing the packet arrival rate. However, with finite buffer sizes, some packets are lost if arrival rate is high. , change the congestion window and retransmit lost packets) thus increasing the arrival rate. In other words, some applications may force one to model a feedback loop that alters the packet arrival rate. The decomposition of an m-server queue into single-server and delay center (Fig. 3) is similar to the Schweitzer Approximation. This decomposition makes it possible to use the MVA equations.
2, an exponential distribution has C = 1. It follows that, for M/M/1, n = ρ + ρ2 1+1 ρ = . 5) From Eq. 1), T = 1 n = . 6) ρ2 . 7) ρ 1 L = . 8) From Eq. 4), L=n−ρ = From Eq. , M/D/1), then C = 0, so n = ρ + ρ2 ρ ρ 1+0 = 1− 2(1 − ρ) 2 1−ρ for M/D/1. 9) Compare this to Eq. 5), and we see that (for the same server utilization ρ) M/D/1 has smaller queue size n. This illustrates the impact of randomness in service times on performance. 18 2. SINGLE QUEUES In fact, for D/D/1, it is easy to see that T = 1 , μ n= λ , μ L=0 and W =0 for any λ ≤ μ.
1. Assume each queue has one or more servers with exponentially distributed service time, and Poisson arrival of jobs to the network. ) This is an example of a Jackson network . If the network has Q queues and if ni is the number of jobs at queue i, then a Jackson network in steady state has the surprising property that Prob(n1 = k1 , . . , nQ = kQ ) = Prob(n1 = k1 ) · · · Prob(nQ = kQ ). 9) In other words, despite queues feeding into one another, the queues behave like they are independent, in the sense that the joint probability in Eq.
Analytical Performance Modeling for Computer Systems by Y.C. Tay