In order to apply the results of formal studies of real-time task models, a practitioner must account for the effects of phenomena present in the implementation but not present in the formal model. We study the feasibility and schedulability problems for periodic tasks that must compete for the processor with interrupt handlers - tasks that are assumed to always have priority over application tasks. The emphasis in the analysis is on deadline driven scheduling methods. We develop conditions that solve the feasibility and schedulability problems and demonstrate that our solutions are computationally feasible. Lastly, we compare our analysis with others developed for static priority task systems.>