By Dr. Samuel H. Fuller (auth.)
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If the queue is emptyj the processor begins a new latency period of time F~ where F is a random v a r i a b l % independent of A and B, with distribution Fr(t). e. the models described by the Pollaczek-Khinchine formula~ is that it no longer assumes the idle state has the memoryless property. 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.
22) This concludes the development of models for the SLTF file drum. Unlike the FIFO file drum 3 the FIFO paging drum~ and the SLTF paging drum~ we do not have a model that is exact; in each of the three models of the SLTF file drum~ assumptions are made that do not exactly reflect the actual behavior of a SLTF file drum. 4. Verification of SLTF file drum models We have presented three different models of the SLTF file drum: the one-stage Markov model; the 2-stage Markov model, and Abate and Dubner's model.
3)~ we approximated Eq. 2) by the exponential (2) we assumed the position of the read-write heads at the end of a record transmission is independent of its position at the start of transmission~ and (3) we assumed that latency is a function only of the current queue length and not influenced by previous queue sizes. 4 but the error introduced by these approximations is slight for large R, and as R becomes small 3 the second assumption causes large overestimations of numbers. However~ for larger 9~ the third approximation, related to Feller's waiting time paradox~ dominates and the error it introduces becomes severe as p ~ 1.
Analysis of drum and disk storage units by Dr. Samuel H. Fuller (auth.)