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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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