We consider a real-time scheduling problem that occurs in the design

of software-based aircraft control. The goal is to distribute tasks

$ au_i=(c_i,p_i)$ on a minimum number of identical machines and to

compute offsets $a_i$ for the tasks such that no collision occurs. A

task $ au_i$ releases a job of running time $c_i$ at each time $a_i +

kcdot p_i, , k in mathbb{N}_0$ and a collision occurs if two jobs are

simultaneously active on the same machine.

We shed some light on the complexity and approximability landscape of this problem.

Although the problem cannot be approximated

within a factor of $n^{1-varepsilon}$ for any $varepsilon>0$, an interesting restriction

is much more tractable: If the periods are dividing (for each $i,j$ one has $p_i |

p_j$ or $p_j | p_i$), the problem allows for a better structured representation of solutions, which leads

to a 2-approximation. This result is tight, even asymptotically.