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By Dr. Samuel H. Fuller (auth.)

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Extra resources for Analysis of drum and disk storage units

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E. Eq. 1). 1. 5 time (drum revolutions) Histogram of latency plus transfer times for a FIFO file drum. 25 25 = 1 - = (i e -~t ; - e -~iT) e-FLIt-T] 0 s; t T The relatively good fit of g(t) to the histogram when ~ = 3/T (R =11/3) indicates the appropriateness of this model of I/O requests and we will use it in our analysis of file drums. e. Poisson arrivals (M)~ general service time (G)~ and one server (I)~ and we can use the Pollaczek- Khinchine formula [cf. Cox and Smith~ 1961 ; Saatyj 1961 ] to give us the expected waiting time of an I/O request at the drum: where T 2 2 C2= 12 (coefficient of variation of service time) (½ + g)%2 For exponentially distributed record lengths~ G = I/R in the above equations and we can achieve some simplifications.

3k 2 Since al]. a position the to previous zero. the records begin one; are servicing this is one sector long, a new r e q u e s t reflected paging immediately in Skinner's This leads to the simplifying the model drum is after in finishing by setting B to result that Fz(t) = FA(t). If the queue is empty after the paging drum finishes servicing a request, it must remain latent for the time to traverse one sector before examining the queue again. Hence, for a paging drt~a F is not a r a n d o m variable at all, it is always T/k, and k F2 = (~)2 g Therefore, the mean waiting time for I/O requests at a FIFO paging d r u m is -- w =[ (21 + I g) 1 + I X(½ + ~-) (1 + ~---~-) -r 1 "r] 3 ['~ - X(½ + ~-ff) The FIFO sectored file drum.

Two-stage Markov model l G of the SLTF file drum. 37 The first of the two servers has service time distribution Gn(t)~ and hence service rate (n+l)/T 3 and models the latency incurred accessing a record when there are n I/O requests demanding service. This 'latency' server is the result of our recent discussion and one further assumption: we assume that the latency is purely a function of queue depth and not related to the past performance of the drum. a very good approximation~ Although this is normally it is not entirely true.

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