Early Deadline First (EDF) scheduling in real-time systems feasibility test proof
I might be too focus on the algebra. I believe I only need to argue or proof a scenario that would give the least density of the system that will fail to meet a deadline.
As shown in the figure below, all tasks start at the same time with same period and deadline. For each of period, each task only have time slot D=D1=D2=...=Dn to execute. In other words, they share exactly the same time slot to execute. If density &gt; 1 then obviously schedule will fail. If the below system has a density of $1^+$(greater than 1 by the smallest amount), then any changes on Di or Pi will only increase the density of the system or make the system feasible.