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System throughput:

X = N/(R + Z) = 1/(6 + 4) = 0.1

Device queue lengths:

QCPU = XRCPUVCPU = 0.1 × 0.125 × 16 0.2
QA = XRAVA = 0.1 × 0.3 × 10 = 0.3
QB = XRBVB = 0.1 × 0.2 × 5 = 0.1

Iteration 2

Number of users: N = 2

Device response times:

RCPU = SCPU(1 + QCPU) = 0.125(1 + 0.2) = 0.15

RA = SA(1 + QA) = 0.3(1 + 0.3) = 0.39

RB = SB(1 + QB) = 0.2(1 + 0.1) = 0.22

TABLE 34.1 MVA Results for Example 34.2

Responce Time Queue Lenths
Iteration
System
No. CPU Disk A Disk B System Throughput CPU Disk A Disk B

1 0.125 0.300 0.200 6.000 0.100 0.200 0.300 0.100
2 0.150 0.390 0.220 7.400 0.175 0.421 0.684 0.193
3 0.178 0.505 0.239 9.088 0.229 0.651 1.158 0.273
4 0.206 0.647 0.255 11.051 0.266 0.878 1.721 0.338
5 0.235 0.816 0.268 13.256 0.290 1.088 2.365 0.388
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
17 0.370 3.962 0.300 47.045 0.333 1.974 13.195 0.499
18 0.372 4.259 0.300 50.032 0.333 1.981 14.187 0.499
19 0.373 4.556 0.300 53.022 0.333 1.987 15.181 0.500
20 0.373 4.854 0.300 56.016 0.333 1.991 16.177 0.500

System response time:

R = RCPUVCPU + RAVA + RBVB = 0.15 × 16 + 0.39 × 10 + 0.22 × 5 = 7.4

System throughput:

X = N/(R + Z) = 2/(7.4 + 4) = 0.175

Device queue lengths:

QCPU = XRCPUVCPU 0.175 × 0.15 × 16 = 0.421
QA = XRAVA = 0.175 × 0.39 × 10 = 0.684
QB = XRBVB = 0.175 × 0.22 × 5 = 0.193

The iterations can be continued for higher values of N. They can be easily implemented using any spreadsheet software package. The response times, throughputs, and queue lengths at the end of these iterations are listed in Table 34.1.

Note that MVA is applicable only if the network is a product form network. This means that the network should satisfy the conditions of job flow balance, one-step behavior, and device homogeneity, as described in Section 32.2. In addition, the analysis, as presented here, assumes that all service centers are either fixed-capacity service centers or delay centers. In both cases, we assumed exponentially distributed service times.


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