An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems

We show a methodology for the computation of the probability of deadline miss for a periodic real-time task scheduled by a resource reservation algorithm. We propose a modelling technique for the system that reduces the computation of such a probability to that of the steady state probability of an infinite state Discrete Time Markov Chain with a periodic structure. This structure is exploited to develop an efficient numeric solution where different accuracy/computation time trade-offs can be obtained by operating on the granularity of the model. More importantly we offer a closed form conservative bound for the probability of a deadline miss. Our experiments reveal that the bound remains reasonably close to the experimental probability in one real-time application of practical interest. When this bound is used for the optimisation of the overall Quality of Service for a set of tasks sharing the CPU, it produces a good sub-optimal solution in a small amount of time.Comment: IEEE Transactions on Parallel and Distributed Systems, Volume:27, Issue: 3, March 201

Probabilistic analysis of bufferless pipelines of real-time tasks

In this paper, we consider real-time applications consisting of multiple tasks, which are executed on computing cores managed by a resource reservatin scheduler. The tasks are organised in a linear topology (pipeline). The result produced by a task as a result of one of its activations is used as input for the task at the next stage of the pipeline. The time required for each execution of a task is a random variable. We assume a bufferless communication semantic, whereby a data item produced by a task is outright dropped if the consumer is not ready to execute. Assuming a bufferless communication simplifies the computation of the probability distribution of the end-to-end delay, since when an item is correctly processed by the pipeline its accumulated delay is simply the sum of the delays incurred in each stage. However, data can be dropped at any stage if the pipeline, and this requires a precedure to compute the probability of such an event. This computation is the main problem addressed in the paper, where we also show the practical applicability of the approach through a set of experiments