Existence of Real-Time Multiprocessor Schedule Does an algorithm exist to check for the existence of a Real-Time Multiprocessor Schedule for aperiodic hard tasks(all of which have the same Release time)?

Assumptions:


The processors are Uniform parallel machines
Job preemption is permitted
Job migration is permitted
Job parallelism is forbidden


EDIT: Let there be $n$ jobs $J = \{j_1, j_2,\text{...}, j_n\}$ and $m$ no of processors $P = \{p_1, p_2,\text{...}, p_m\}$. Each job $j_i$ has a task time $t_i$(amount of work it would take to complete it) and due time $d_i$. Each processor has a constant speed $s_i$(amount of work it does per unit time). Each task must be completed before its due time. 

I am interested to know about an algorithm with can check feasibility of a schedule in polynomial time.
Y. Cho and S. Sahni, Scheduling Independent tasks with due times on a uniform Processor System, Jr. of the ACM, 1980


Presents an algorithm to preemptively schedule n tasks(with due dates) on m uniform processors whenever a solution exists in $O(n\log{n} + mn)$ time. 

Which is a stronger problem than I wanted to solve but still gives a polynomial algorithm, which answers my question.