Executive Summary

In this paper, the authors propose a novel approach to quantify execution time variability of programs using statistical dispersion parameters. They go on to discuss how this variability can be leveraged in mixed criticality real-time systems, and introduce a heuristic for computing the execution time budget for low criticality real-time tasks based on their variability. Through experiments and simulations, the authors demonstrate that their proposed heuristic reduces the probability of exceeding the allocated budget compared to algorithms that do not consider execution time variability.

Analysis and Commentary

The authors’ focus on quantifying execution time variability and its impact on real-time systems is a valuable contribution to the field. Real-time systems often have tasks with different criticality levels, and efficiently allocating execution time budgets is crucial for meeting deadlines and ensuring system reliability.

The use of statistical dispersion parameters, such as variance or standard deviation, to quantify execution time variability is a sensible approach. By considering the spread of execution times, rather than just the average or worst case, the proposed method captures a more comprehensive view of program behavior. This helps in decision-making related to resource allocations and scheduling.

The introduction of a heuristic for computing execution time budgets based on variability is a practical solution. By considering each task’s execution time variability, the proposed heuristic can allocate more accurate and realistic budgets. This reduces the probability of exceeding budgets and helps prevent performance degradation or missed deadlines in mixed criticality contexts.

The experiments and simulations conducted by the authors provide objective evidence of the benefits of incorporating execution time variability into budget allocation decisions. By comparing their proposed heuristic with other existing algorithms that disregard variability, the authors demonstrate that their approach leads to a lower probability of exceeding budgets. This supports their claim that considering variability improves system reliability and performance.

Potential Future Directions

The research presented in this paper opens up several potential future directions for exploration and enhancement:

  1. Integration with formal verification techniques: While the proposed heuristic shows promising results, further work could be done to integrate it with formal verification techniques. By combining the quantification of execution time variability with formal methods, it would be possible to provide stronger guarantees and proofs of correctness for real-time systems.
  2. Adaptive budget allocation: The current heuristic computes static budgets based on a task’s execution time variability. However, future research could explore adaptive approaches where budgets are dynamically adjusted based on real-time observations of task execution times. This could improve resource utilization and adapt to changing system conditions.
  3. Consideration of other factors: While execution time variability is an important factor, there are other aspects that can impact real-time systems’ performance and reliability, such as cache effects or inter-task dependencies. Future work could investigate how to incorporate these additional factors into budget allocation decisions to further enhance system behavior.


The paper presents a valuable contribution in the field of mixed criticality real-time systems by proposing a method to quantify execution time variability using statistical dispersion parameters. The introduction of a heuristic for allocating execution time budgets based on this variability improves system reliability and reduces the probability of exceeding budgets. The experiments and simulations conducted provide empirical evidence supporting the benefits of considering execution time variability. The research opens up potential future directions for further exploration and enhancement, including integration with formal verification techniques, adaptive budget allocation, and consideration of other factors that affect real-time system performance.

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