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U. Glaeser

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Access Time [ms]<br />

2<br />

0<br />

0<br />

FIGURE 8.6 Measured and computed access times. (From Dujmovic, J., Tomasevich, D., and Au-Yeung, M., Proc.<br />

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

FIGURE 8.7 Measured and computed access times showing the cache size of 48 MB (magnified detail of Fig. 8.5).<br />

(From Dujmovic, J., Tomasevich, D., and Au-Yeung, M., Proc. CMG, 1999, Reno, NV. With permission.)<br />

If we measure disk access times T 1,…,T n for a sequence of file sizes F 1,…,F n, the calibration of the<br />

above model can be performed by selecting the optimum values of T cache, C, r, and T max seek, which<br />

minimize the criterion function<br />

The exponent q is usually selected in the range 1 ≤ q ≤ 4, where larger values are selected in cases<br />

where the primary goal is to minimize large errors. The minimization can be performed using the<br />

traditional Nelder–Mead simplex method [8].<br />

A verification of this model is shown in Figs. 8.6 and 8.7 for a 300 MHz PC with 64 MB of memory,<br />

Windows NT 4.5, and a 4-GB SCSI disk that has N nev = 7200 rev/min. The resulting parameters are T cache =<br />

96 µs, C = 48 MB, r = 0.234, and T max seek 7.51 ms for F max = 1400 MB. In the majority of 245 measured points<br />

(only some of them shown in Fig. 8.6) the mean relative error of this model is less than 1%.<br />

Disk Access Optimization Model<br />

14<br />

12<br />

10<br />

Access Time [ms]<br />

8<br />

6<br />

4<br />

5<br />

4.5<br />

4<br />

3.5<br />

3<br />

2.5<br />

2<br />

1.5<br />

1<br />

0.5<br />

0<br />

0<br />

20<br />

500<br />

1000<br />

File Size [MB]<br />

Measured<br />

Computed<br />

40 60 80<br />

File Size [MB]<br />

Computed<br />

Measured<br />

The disk access time model described in the previous section assumes a single program that generates<br />

disk access requests. In such a case, all requests are served strictly in the order they are submitted and<br />

disk access optimization is not possible; however, in the case of multiprogramming, the disk queue<br />

contains multiple requests independently generated by various programs. It is possible to use a disk access<br />

optimization algorithm that increases the global disk throughput by minimizing the movement of I/O<br />

head mechanism. The simplest such an algorithm is the “shortest seek time first” (SSTF) [13,14], which<br />

can be easily analyzed.<br />

© 2002 by CRC Press LLC<br />

n<br />

∑<br />

100<br />

1500<br />

E( Tcache, C, r, Tmax seek)<br />

= Ti – Ta( Fi, Tcache, C, r, Tmax seek)<br />

i=1<br />

120<br />

q

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