U. Glaeser

1400
1200
1000
FIGURE 8.13 Measured response times and the results of the LDMVA model. (From Dujmovic, J., Tomasevich,
D., and Au-Yeung, M., Proc. CMG, 1999, Reno, NV. With permission.)
benchmarks accessing a 100 MB file and 1 GB file are presented in Fig. 8.13. The LDMVA model we used
is based on measured disk parameters reported in the “Numerical Computation of the Average Seek
Time” section and on the disk service time model Sd(F, n) proposed in the section on “Disk Access
Optimization Model.” Disk accesses to a file of size F occur with the probability (F − C)/F and cache
accesses with the probability C/F. The number of disk visits Vd now depends on the number of processor
visits Vp and the size of file. If the number of disks is k then Vd(F) = Vp(F − C)/kF. Therefore, the disk
cache causes both the disk service time and the number of visits to be functions of the file size. Processor
prog cache
service time is not constant. For cache accesses it can be expressed as Sp = tp + tp and for disk accesses
prog cache disk
as Sp = tp + tp + tp , where the three components correspond to the processor activity for the
benchmark program, cache access, and serving the file management system during the disk access. The
prog cache disk
mean service time is Sp = tp + tp + tp (F − C)/F. The calibrated model in Fig. 8.13 has the mean
modeling error of 7.4%.
Predictive Power of Queuing Models
Response Time [seconds]
Measured (F=100 MB)
Measured (F=1 GB)
800
600
400
200
Model (F=100 MB)
Model (F=1 GB)
0
0 5 10 15 20
Degree of Multiprogramming N
All queuing models have adjustable parameters (e.g., the processor and disk service times). The default
values of these parameters, taken from manufacturers specifications, regularly yield rather large prediction
errors. These errors can be reduced by corrections of parameters in a calibration process. During the
model calibration the parameters are adjusted to minimize the difference between the measured values
and computed values from the model. In essence, this is just a standard curve fitting process, and the
resulting low description error is not necessarily a proof of the quality of the model. The only way to
assess the quality of the model is through the analysis of the prediction errors.
Let n be the number of measured response times R 1,…,R n and let us use the first m measured values,
R 1,…,R m, m ≤ n, for the model calibration. The indicator p = 100 m/n shows the percent of values used
for calibration. Let e(p) denote the average relative error between the measured vales and the values of
the calibrated model for the whole range of n data points. Generally, e(p) is expected to be a decreasing
function, and three typical such functions are presented in Figs. 8.14 and 8.15.
In all cases, we measured the processor time and used this value in our LDMVA model. The calibration
process included three parameters of the disk subsystem (minimum service time t min, maximum service
time t max, and the exponent α introduced in the section on “A Simple Model of Cached Disk Access
Time”). Consequently, the e(p) function starts with m = 3 points.
© 2002 by CRC Press LLC