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Response Time [seconds]<br />

290<br />

270<br />

250<br />

230<br />

210<br />

190<br />

170<br />

150<br />

Computed R1 Measured R1<br />

Computed R2 Measured R2<br />

1 3 5 7 9 11 13 15 17 19<br />

Degree of Multiprogramming<br />

FIGURE 8.12 The results of LDMVA model calibration. (From Dujmovic, J., Tomasevich, D., and Au-Yeung, M.,<br />

Proc. CMG, 1999, Reno, NV. With permission.)<br />

Experimental Results for LDMVA Model of a Disk Subsystem<br />

with Access Optimization<br />

Let us now apply the LDMVA model for the VAX 8650 disk subsystem modeling. The measured response<br />

and processor times can be used to adjust parameters of the LDMVA model. This is called calibration<br />

of the queuing model. The calibration process is based on measured response times T m1(n) and T m2(n),<br />

which correspond to systems with one and two disk controllers. Suppose that the load dependent disk<br />

service time is approximated by S d(n) = t min + (t max − t min)e α(n−1) . The parameters of the LDMVA model<br />

are t min, t max, α, S p, S c. Let R c1(n, t min, t max, α, S p, S c) and R c2(n, t min, t max, α, S p, S c) be the response times<br />

computed from the LDMVA model, respectively using one and two controllers. The model calibration<br />

procedure is based on the minimization of the compound criterion function<br />

C( tmin, tmax, a, Sp, Sc) n<br />

max [ Tm1( n)<br />

– Rc1( t .<br />

min tmax, a, Sp, Sc) ] 2 , [ Tm2( n)<br />

– Rc2( t .<br />

min tmax, a, Sp, Sc) ] 2<br />

⎛ ⎞<br />

= ⎜∑∑⎟ ⎝ ⎠<br />

i=1<br />

The results of calibration performed using the Nelder-Mead simplex method [8] are the following<br />

values of parameters: t min = 11.5 ms, t max = 20 ms, a = −4, S p = 0.822 ms, and S c = 0.89 ms. The mean<br />

relative error for all presented points is 1% (Fig. 8.12). At this level of description error it is realistic to<br />

expect good prediction results.<br />

Experimental Results for LDMVA Model of a Disk Subsystem<br />

with Caching and Access Optimization<br />

In this experiment, we use the same 300 MHz PC presented in the “Numerical Computation of the<br />

Average Seek Time” section and Figs. 8.6 and 8.7. Its memory capacity is 64 MB with two disk units,<br />

and the disk cache size under Windows NT 4.5 is C = 48 MB. The measured response times for DRAN<br />

© 2002 by CRC Press LLC<br />

n<br />

i=1

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