By Dr. Samuel H. Fuller (auth.)
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Additional info for Analysis of drum and disk storage units
It is interesting~ even if for comparative purposes only, to briefly discuss a simplification of the two-stage model. 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_ !
2 is a similar plot except the expected records size is 1/8 of the drum's circumference. We use l/3 because this is close to the measured value of record sizes discussed in Sec. 2 and 1/8 because Abate and Dubner thought their model should be a good approximation for < i/4. 4~ the results are encouraging: the two- stage model tracks the simulated waiting time very closelyj but is a slight overestimate; the one-stage model follows the simulation fairly closely but is more of an overestimate than the two-stage model; and Abate and Dubner's model is an u n d e r e s t i m a t % but they warned their model might not apply very accurately for R > I/~.
And the underestimates become increasingly The following illustration gives an intuitive explanation for this phenomena. requests. as well as Abate From the arguments Suppose we have n outstanding that lead to Eq. 3) we know the expected distance from the read-write heads to the first starting address is i/(n+l). However~ the reasoning can be applied to distances opposite to the drum's rotation and again the distance from the read-write heads to the closest starting address behind the read-write heads is I/(n+l).