Download Analysis of drum and disk storage units by Dr. Samuel H. Fuller (auth.) PDF

By Dr. Samuel H. Fuller (auth.)

ISBN-10: 0387071865

ISBN-13: 9780387071862

ISBN-10: 3540071865

ISBN-13: 9783540071860

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Sample text

An Empirical Model of, the SLTF,,,File Drum In this section we develop a simple~ empirical expression for the expected waiting time of the SLTF file drum. Such an empirical expression has a limited utility, but in conjunction with the other models available for the SLTF file drum it can be a useful tool. The expressions fur the expected waiting time for the FIFO file drum, the FIFO paging d~,m~ the SLTF paging dn~m, and Abate and Dubner's model of the SLTF file drum all have the basic hyperbolic form: 53 = {½ + R + b(l~Pp)]T and c o n s e q u e n t l y file drum.

The 41 0 u4 > 0 o Ii , ! 1 by a single Fig. rate. is to replace the two series-coupled exponential server with the same mean servers service Let Mn denote the mean service rate of the single server when there are n I/O requests in the queue, then I T ~n = I ~ - + - f + -- ~T + n + l = ~(~ + i) It follows in a straightforward analogous to Eqs. 7), for the one-stage model, PO = manner that the balance equations are ~I Pl ' (3"i~) (k + ~n)Pn = kpn_ ! + ~n+l Pn+l ' The above set of recurrence forward substitution relations n = 1,2~...

A and related topics~ are discussed by Feller [1970] under the general heading of waiting-time paradoxes. Let us consider in more detail why the two-stage model underestimates the wait time. Let S(1), S(2), and S(3 ) denote the starting addresses in order of increasing distance from the read-write head~ denoted H~ and let F(I ) be the finishing address of the record beginning with S(I ). Let F(I ) be a random variable uniformly distributed around the circumference of the drum~ and for this example suppose it is independent o~ S(1 ).

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