We show a methodology for the computation of the probability of deadline missfor a periodic real-time task scheduled by a resource reservation algorithm. Wepropose a modelling technique for the system that reduces the computation ofsuch a probability to that of the steady state probability of an infinite stateDiscrete Time Markov Chain with a periodic structure. This structure isexploited to develop an efficient numeric solution where differentaccuracy/computation time trade-offs can be obtained by operating on thegranularity of the model. More importantly we offer a closed form conservativebound for the probability of a deadline miss. Our experiments reveal that thebound remains reasonably close to the experimental probability in one real-timeapplication of practical interest. When this bound is used for the optimisationof the overall Quality of Service for a set of tasks sharing the CPU, itproduces a good sub-optimal solution in a small amount of time.
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