How do you determine whether a set of tasks will meet their deadlines?

Through schedulability analysis, which combines each task's worst-case execution time, period, and deadline. The first, simplest check is CPU utilization: sum each task's WCET divided by its period; if that total exceeds 1.0 (100%) the task set is definitely infeasible, and even below that you need to be under the relevant bound. Under fixed-priority scheduling, the classic approach is Rate-Monotonic Scheduling: assign priorities by period, the task with the shortest period gets the highest priority (more frequent equals more urgent), and there's a utilization bound (around 69% as the number of tasks grows, often higher in practice) below which all deadlines are guaranteed; for utilizations between that bound and 100% you use the more precise response-time analysis, which iteratively computes each task's worst-case response time including interference from higher-priority tasks and blocking from lower-priority ones (priority inversion), and checks it against the deadline. The dynamic-priority alternative is Earliest Deadline First, which always runs the task with the nearest deadline and can theoretically reach 100% utilization (more efficient) but is more complex to implement and degrades unpredictably under overload. The practical guidance is to assign priorities by urgency (RMS), keep utilization comfortably below the bound to leave margin for jitter and interrupts, include blocking time from shared resources in the analysis, and verify with both analysis and measurement. You don't just hope it fits, you compute whether it does.