Comments on "Multiprocessor Scheduling with Memory Allocation–A Deterministic Approach"

In the above paper1 the author has investigated a problem of the preemptive scheduling of n independent tasks T = {T1, T2, ···, Tn} on m identical uniprogrammed CPU´s P1, P2, ···, Pmwhen a common primary memory of N pages is available. Each task Tiis specified by the virtual time vi and the progress rate pi(si) where si is the number of primary memory pages allotted to Ti. The vector s̄(t) = (S1(t),S2(t),···, Sn(t)) (Si(t)≥0 for 1 ≤ i ≤ n, t ≥ 0; Σi=1 n Si(t) ≤ N for every t; nt0 y pi(si(t))dt = vifor 1 ≤ i ≤ n)[/mi] is determined for which the schedule length y is minimal. The numbers of primary memory pages allotted to tasks are treated as continuous variables.