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An evaluation of approaches to model checking real-time task schedulability analysis

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  • Special Issue: SPIN 2021
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Abstract

This article is a follow-up contribution that extends the conference paper (Nxumalo, in: Laarman, Sokolova (eds)Model Checking Software - 27th International Symposium, 2021) which presented the spotlight abstraction method to enable an efficient model checking of schedulability properties of real-time operating systems. Our approach is based on iterative spotlight abstraction whereby the real-time task queue is divided into a so-called spotlight and a shade. Initially, an abstract state space model is generated from the spotlight, which contains a small number of tasks that appear at the front of the queue and the shade contains the remaining tasks. The schedulability of the spotlight tasks is model checked, whereas the behavior of the shade is summarized, and the result is saved for later re-use. If this result is still inconclusive, more tasks are iteratively brought from the shade into the spotlight, with which the model checker can proceed. These steps are repeated until a decisive schedulability result is obtained. In this article, we enrich the encoding of real-time systems into timed automata by separating operations over clock variables from operations based on other variables such as Boolean and integers. We enforce to maintain a reasonable size of the spotlight model by applying counter abstraction to the tasks that were previously confirmed schedulable in the previous iterations. We compare our approach against Timestool and RTLib, an Uppaal template, in the analysis of the schedulability of real-time tasks for the First-In-First-Out and Shortest-Deadline-First scheduling policies. Empirical results show that our approach can handle more tasks than Timestool and RTLib.

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Notes

  1. To avoid any mis-understanding at this point: Our analysis technique is designed only for those systems which can be completely analyzed ‘statically’ before their actual deployment; here, we are thus not dealing with any ‘on-the-fly’ schedulability analysis at run-time by means of an auxiliary analysis process within the ‘core’ of some rtos itself. For this reason, the queue in our formal model contains only formal representations of the tasks of interest (instead of actual processes in the form of their concrete process control blocks).

  2. Worst case of the analysis: The entire queue is eventually in the spotlight and the shade is \(\{\}\).

  3. We borrow the notation assume(e) from three valued model checking where assume(e) is a guard and e is an expression.

  4. Setting the run-time of a task to 0 at ‘enqueue’ presumes a FIFO scheduling system in which it is not; possible to re-enqueue an un-finished task.

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  1. University of Pretoria, Pretoria, South Africa

    Madoda Nxumalo, Nils Timm & Stefan Gruner

  2. University of Eswatini, Kwaluseni, Eswatini

    Madoda Nxumalo

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Nxumalo, M., Timm, N. & Gruner, S. An evaluation of approaches to model checking real-time task schedulability analysis. Int J Softw Tools Technol Transfer 25, 115–128 (2023). https://doi.org/10.1007/s10009-022-00693-9

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