Optimal Rules And Algorithms for Some Parallel Processor Scheduling Problems

Cover Optimal Rules And Algorithms for Some Parallel Processor Scheduling Problems
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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