You are required to read and agree to the below before accessing a full-text version of an article in the IDE article repository.

The full-text document you are about to access is subject to national and international copyright laws. In most cases (but not necessarily all) the consequence is that personal use is allowed given that the copyright owner is duly acknowledged and respected. All other use (typically) require an explicit permission (often in writing) by the copyright owner.

For the reports in this repository we specifically note that

  • the use of articles under IEEE copyright is governed by the IEEE copyright policy (available at http://www.ieee.org/web/publications/rights/copyrightpolicy.html)
  • the use of articles under ACM copyright is governed by the ACM copyright policy (available at http://www.acm.org/pubs/copyright_policy/)
  • technical reports and other articles issued by M‰lardalen University is free for personal use. For other use, the explicit consent of the authors is required
  • in other cases, please contact the copyright owner for detailed information

By accepting I agree to acknowledge and respect the rights of the copyright owner of the document I am about to access.

If you are in doubt, feel free to contact webmaster@ide.mdh.se

On the Convolution Efficiency for Probabilistic Analysis of Real-Time Systems

Fulltext:


Publication Type:

Conference/Workshop Paper

Venue:

33rd Euromicro Conference on Real-Time Systems

Publisher:

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik

DOI:

10.4230/LIPIcs.ECRTS.2021.16


Abstract

This paper addresses two major problems in probabilistic analysis of real-time systems: space and time complexity of convolution of discrete random variables. For years, these two problems have limited the applicability of many methods for the probabilistic analysis of real-time systems, that rely on convolution as the main operation. Convolution in probabilistic analysis leads to a substantial space explosion and therefore space reductions may be necessary to make the problem tractable. However, the reductions lead to pessimism in the obtained probabilistic distributions, affecting the accuracy of the timing analysis. In this paper, we propose an optimal algorithm for down-sampling, which minimises the probabilistic expectation (i.e., the pessimism) in polynomial time. The second problem relates to the time complexity of the convolution between discrete random variables. It has been shown that quadratic time complexity of a single linear convolution, together with the space explosion of probabilistic analysis, limits its applicability for systems with a large number of tasks, jobs, and other analysed entities. In this paper, we show that the problem can be solved with a complexity of O(n log(n)), by proposing an algorithm that utilises circular convolution and vector space reductions. Evaluation results show several important improvements with respect to other state-of-the-art techniques.

Bibtex

@inproceedings{Markovic6263,
author = {Filip Markovic and Alessandro Papadopoulos and Thomas Nolte},
title = {On the Convolution Efficiency for Probabilistic Analysis of Real-Time Systems},
editor = {Bj{\"o}rn B. Brandenburg},
month = {July},
year = {2021},
booktitle = {33rd Euromicro Conference on Real-Time Systems},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
url = {http://www.es.mdh.se/publications/6263-}
}