Optimal Rules And Algorithms for Some Parallel Processor Scheduling Problems

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Optimal Rules And Algorithms for Some Parallel Processor Scheduling Problems
Martin-Vega, Louis Anthony
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m and t = 1,2,. . .H where is the number of MCMs available during period t and q. is defined to be zero for 1 = 1,2,... in.
The system can be modeled as a directed network by creating nodes n for t = 1,2,... II and p. for 1 = l,2,...m and t = 1,2,...!!.
For t = 1,2,...H, construct an arc from n to p with capacity ci t it - M it and associate a loss probability of zero with each of these arcs.
For t = 1,2, ...H-l, and i = 1,2,... in, construct an arc from p to F it P; i-4-i with capacity ) q and
... loss probability I. (f(p ,p )) i>c-t-i ^_, iic - x t ^ it i,t+l k=l where ( r '(p i( _, P.. t+1 ) ) is the arc flow. Construct a source node 3 with arcs from S to n having capacities Q and loss probabilities of zero for t = 1,2,...H, and a sink node T with arcs from p to i ,H H T with capacities |. and loss probabilities Z (f(p , T) ) it r it w iH t = l L2i (Loss Probability, Capacity, lower Bound) (0,q u ,0) U u (.), qil ,o) (0,Q 1 ,0) (0,Q 3 ,0) (0,q 23 ,0) Figure 4: Network Representation of a Two Port Three Period Min-Max Loss Probability Allocation Problem 129 for i = l,2,...m.

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