By Dr. Samuel H. Fuller (auth.)
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Additional info for Analysis of drum and disk storage units
In the analysis of the two-stage model of an SLTF file drum just discussed, a concerted attempt was made to closely approximate the behavior of the drum. 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.
1o) the latency is the distance - Ln-i 1 = 2 1 . n+---~ " n+2 + n+l n+4 + n-i n+l Hence i n+2 1 = ~(n+2)(n÷i) The above inequality 3 n42 from F(I ) to S(j+I ). > n illustrates that latency is dependent on the past history of the drum; and that unlike the SLTF and FIFO paging drums~ as well as the FIFO file drumj the SLTF file drum does not experience Markov epoch upon completion of an I/O request. The only instances a in which the drum's future performance truly uncouples from the past behavior is when the drum is idle.
910 The above discussion makes no mention of how well the higher order moments (greater than 2) of Gn(t ) approximate Fn(t ). However~ we feel somewhat justified in ignoring these higher moments since both the Pollaczek-Khinchine formul% Eq. 2)~ and the Skinner formula~ Eq. 4),show that the expected waiting time (and queue size) is only a function of the first two moments of the service time. neither the Pollaczek-Khinchine or Skinner formulas directly apply here since service timej in particular latency~ However, Unfortunstely is queue size dependent.
Analysis of drum and disk storage units by Dr. Samuel H. Fuller (auth.)