Real-Time Applications with Stochastic Task Execution Times presents three approaches to the analysis of the deadline miss ratio of applications with stochastic task execution times. Each of the three approaches fits best to a different context. The first approach is an exact one and is efficiently applicable to monoprocessor systems. The second approach is an approximate one, which allows for designer-controlled trade-off between analysis accuracy and analysis speed. It is efficiently applicable to multiprocessor systems. The third approach is less accurate but sufficiently fast in order to be placed inside optimisation loops. Based on the last approach, we propose a heuristic for task mapping and priority assignment for deadline miss ratio minimisation.