Edge resources can provide a cost-effective and confidential alternative to cloud computing when resource-constrained devices require high computing power. For time-critical applications such as pervasive simulations, they also have the advantage of geographical proximity resulting in reduced latency. The management of edge resources in a decentralized manner, however, makes it challenging to obtain a global view in real-time, which in turn leads to scheduling decisions being made based on incomplete information. This results in suboptimal load balancing and, in the worst case, to deadlines not being met. In this talk, I will discuss different approaches to scheduling time-critical tasks in heterogeneous systems with an emphasis on probabilistic scheduling in decentralized environments to better achieve deadlines. Furthermore, in the talk I will highlight the unique of edge resources, especially end-user devices, and show how they can be used in highly time-critical application contexts.