By Dr. Samuel H. Fuller (auth.)
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Extra resources for Analysis of drum and disk storage units
Let E o2n our model is a birth-and-death Markov be the state where n I/O requests are queued or in service and the latency server~ idle state. Similarly~ define EO~ 0 as the let El, n be the state with n I/O requests and the transmission server~ of being in state E. server O~ is active; server l~ active. If Pi~j(t) is the probability . ; P~,n(t) = -(k+~) P l , n ( t ) + k Pl, n _ l ( t ) + n+l T Po, n (t)' n = 2,3,... In this article we are primarily interested in the steady state solution~ or more precisely~ the solution at statistical equilibrium.
1) we can see that Pr(L n = t) = (n+l)(l-t) n , 0 ~ t < T and = T/n+l n and this is precisely what we found ~ to be by a much simpler argument n M in Sec. 3- However~ now consider Ln_ 1 in the same example. 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 SLTF paging drum. For the analysis of an SLTF paging drum~ let us use the same notation that was developed for the FIFO paging drum~ as well as the same assumptions concerning the I/O requests: all requests 32 are for records directed to the queue the entire It any shown with as k sectors. for the I/O queue period of since neither the drum z2 = B~ of time to start F is the time drum is F is found 3 T. FIFO be Fig. sector~ Poisson is of to to sector after and Interpreting variable. 2 the process let B = finishing of hence Fig.
Analysis of drum and disk storage units by Dr. Samuel H. Fuller (auth.)