By Dr. Samuel H. Fuller (auth.)
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Extra resources for Analysis of drum and disk storage units
It appears likely that the first two moments of the service time are also the dominant parameters in a SLTF file drum and comparison of models based on the exponential approximation to latency shown in Sec. ~ behave very similarly to models not using the approximation. 1 is the model of a SLTF file drum based on the assumptions discussed above. We have a Poisson arrival process with parameter ~, a single queue~ and the server is made up of two exponential servers in series. The second server, with servicing rate ~j models the transmission of records and reflects our assumption of exponentially distributed record lengths.
The only points in time that enjoy the Markovian property in the Skinner model are those instants at which the processor inspects the queue. 4) l'H~pital~s rule must be applied twice to find the limit as s ~ O. The interpretation of Skinner's model as a FIFO paging drum is straightforward. From the assumptions that the starting addresses are independent random variables that are equally likely to have the value of any of the k sector boundaries and all records are one sector long it follows that 29 FA(t) = [ O~i~k-1 where U (x) is the unit step function: N (x) I = I for x ~ 0 for 0 x < 0.
4) line when p l o t t e d as a f u n c t i o n of as a f u n c t i o n p. Clearly of p. the simulation results are not growing as fast as Eq. 3) suggests and it overestimates the rate of growth of W as p ~ 1. i. 8 transformed to test hyperbolic dependence on (l-p). 4 ONE- STAGE MARKOVMODEL----~ /- SIMULATION M O D E I . 2. 6 time for the s i m u l a t i o n model. transformations P i P [~-(,/2+.. 0 01 03 56 Another expression for W that may lead to an adequate empirical model is = (>>) In Fig.
Analysis of drum and disk storage units by Dr. Samuel H. Fuller (auth.)