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DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

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Manuscript for IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 19<br />

weights <strong>and</strong> in proportional allocation (XX-PA) proportional to the components’ load indices as<br />

in (15). PC-PA is the control policy corresponding to the programming model we have<br />

developed. The system makes decision every 100 time units.<br />

Table 2. Control policies used for experimentation<br />

Control policy<br />

F2-RR<br />

F2-PA<br />

F3-RR<br />

F3-PA<br />

F4-RR<br />

F4-PA<br />

F5-RR<br />

F5-PA<br />

PC-RR<br />

PC-PA<br />

Description<br />

v i = 2 for all i with round-robin allocation<br />

v i = 2 for all i with proportional allocation<br />

v i = 3 for all i with round-robin allocation<br />

v i = 3 for all i with proportional allocation<br />

v i = 4 for all i with round-robin allocation<br />

v i = 4 for all i with proportional allocation<br />

v i = 5 for all i with round-robin allocation<br />

v i = 5 for all i with proportional allocation<br />

Predictive control with round-robin allocation<br />

Predictive control with proportional allocation<br />

5.2 Results<br />

Numerical results from the experimentation are shown in Table 3. PC-PA gives the best<br />

performance close to QoS UB in all different conditions. As the cost of completion time increases<br />

the system under PC-PA completes earlier as a result of trading off between the value of solution<br />

<strong>and</strong> the cost of completion time. There can be seen many cases in which the value of solution<br />

under PC-PA is even larger in spite of less completion time. It is because the programming<br />

model gives the maximal value of solution for a given completion time.<br />

Though both PC-PA <strong>and</strong> PC-RR choose value modes by solving the optimization model in<br />

(14), PC-RR gives worse performance because the optimization model is built presuming<br />

proportional resource allocation. Proportional allocation shows significant advantages compared<br />

to round-robin allocation in all thirty instances of comparison. The superiority supports the<br />

optimality of proportional resource allocation <strong>and</strong> consequently the effectiveness of the<br />

programming model.

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