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Computing nmin the pseudo-code). We now discuss the pseudo-code in greater detail. We are given the size of the workload (σ), the amount of time between the current instant and the deadline (∆), the cluster parameters Cp and Cm , and the processor ready times r1 , r2 , . .. We will determine the minimum number of processors needed (nmin ), the shares allocated to each processor (the αi ’s), and the time at which each processor will begin receiving data from the head node Po (the si ’s). The pseudo-code uses two additional variables — alloc, denoting the fraction of the workload that has not already been allocated, and i, indicating that Pi is being considered.

Let assume that g < GCD(T (o1 ), T (o2 )) and without loss of generality we assume also that S(o1 ) = 0. Tasks o1 and o2 cannot be scheduled means that it exists two integers x, y for which Example 1 In figure 1 we applied the previous algorithm on a system of tasks composed of five periodic tasks: (a : 1, 4), (b : 1, 6), (c : 1, 8), (d : 1, 12), (e : 1, 12) connected by some precedences (see figure 1-1=). We consider a scheduling on the hyper-period of these tasks which is the LCM (4, 6, 8, 12) = 24.

We will determine the minimum number of processors needed (nmin ), the shares allocated to each processor (the αi ’s), and the time at which each processor will begin receiving data from the head node Po (the si ’s). The pseudo-code uses two additional variables — alloc, denoting the fraction of the workload that has not already been allocated, and i, indicating that Pi is being considered. The main body of the pseudo-code is an infinite while loop, from which the only exit is be one of two break statements.

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