We investigate deadline meeting properties of the well-known preemptive ลฝ . static priority scheduling SPS algorithm, which is widespreadly used in commercial real-time operating system kernels. A discrete-time single server queueing system employing SPS for scheduling probabilistically arriving tasks at L priority levels is considered for this purpose. ลฝ . ลฝ . ลฝ . Model parameters are arrival and execution-time distribution A z , L z and a constant l l l l ลฝ deadline T g T T per level l. By means of a combinatorial technique which does not require l l L .
ลฝ . stable-state assumptions , we determine the probability distribution of the random-time the system operates without violating any task's deadline. This distribution is asymptotically exponential with parameter , which decreases exponentially with the deadlines T T ; simple T T L L ลฝ . asymptotic expressions for and all associated quantities probabilities, moments, . . . for T T L large T T are provided. Our numerical examples suggest that real-time systems based on SPS L ลฝ . operate reasonably well only if computing performance is more than adequate. แฎ 1997