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U. Glaeser

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FIGURE 8.11 A family of LIMVA models and measured VAX 8650 response time. (From Dujmovic, J., Tomasevich,<br />

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

and yielding disk demands in the range, 6 s ≤ D d ≤ 12 s. The corresponding response times presented in<br />

Fig. 8.11 are, in the whole range, practically straight lines and obviously inadequate for representing the<br />

measured response time function. The best approximation would be obtained for S d = 16 ms, but this<br />

approximation is equally poor as the attempt to use a straight line to approximate a parabola. The nature of<br />

the dynamic behavior of VAX 8650 is quite different from what can be modeled by LIMVA regardless how<br />

well we adjust its parameters. Thus, a more flexible model is needed. Taking into account that disks are never<br />

load-independent, because they regularly use either access optimization or access optimization and caching,<br />

we hope that better results should be expected from load dependent MVA models.<br />

For batch systems we apply the load dependent mean value analysis model (LDMVA) introduced in<br />

[1] (see also [5,7]):<br />

for n = 1 to N do<br />

end_for<br />

n<br />

∑<br />

Response Time [seconds]<br />

450<br />

400<br />

350<br />

300<br />

250<br />

200<br />

150<br />

100<br />

S d =12,13,…,24 ms<br />

50<br />

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

Degree of Multiprogramming<br />

Pk( 00)<br />

= 1, k = 1,…,K<br />

Rk( n)<br />

= jSk( j)Pk(<br />

j – 1 n – 1),<br />

k = 1,…,K<br />

j=1<br />

K<br />

∑<br />

R( n)<br />

= Vk Rk( n)<br />

k=1<br />

X( n)<br />

= n/R( n)<br />

Pk( j/n )<br />

© 2002 by CRC Press LLC<br />

⎧VkSk( j)X(<br />

n)Pk(<br />

j – 1 n – 1),<br />

j = 1,…,n ⎫<br />

⎪ ⎪<br />

n = ⎨ ⎬,<br />

k = 1,…,K<br />

⎪1– ∑P<br />

k( jn),<br />

j = 0 ⎪<br />

⎩ i=1<br />

⎭<br />

n<br />

∑<br />

Qk( n)<br />

= jPk( jn),<br />

k = 1,…,K<br />

j=1<br />

Qk( n)<br />

= 1 – Pk( 0 n),<br />

k = 1,…,K

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