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

TL;DR

This paper introduces a method to analytically compute and bound the probability of deadline misses in reservation-based soft real-time systems, enabling efficient QoS optimization.

Contribution

It presents a novel modeling approach using Markov chains and derives a closed-form conservative bound for deadline miss probability, improving analysis efficiency.

Findings

Bound remains close to actual miss probability in practical scenarios.

The bound enables quick sub-optimal QoS optimization.

The methodology reduces computational complexity for real-time system analysis.

Abstract

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.