Safe and Optimal Scheduling for Hard and Soft Tasks

Authors Gilles Geeraerts, Shibashis Guha, Jean-François Raskin

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Gilles Geeraerts
  • Université libre de Bruxelles, Brussels, Belgium
Shibashis Guha
  • Université libre de Bruxelles, Brussels, Belgium
Jean-François Raskin
  • Université libre de Bruxelles, Brussels, Belgium

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Gilles Geeraerts, Shibashis Guha, and Jean-François Raskin. Safe and Optimal Scheduling for Hard and Soft Tasks. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We consider a stochastic scheduling problem with both hard and soft tasks on a single machine. Each task is described by a discrete probability distribution over possible execution times, and possible inter-arrival times of the job, and a fixed deadline. Soft tasks also carry a penalty cost to be paid when they miss a deadline. We ask to compute an online and non-clairvoyant scheduler (i.e. one that must take decisions without knowing the future evolution of the system) that is safe and efficient. Safety imposes that deadline of hard tasks are never violated while efficient means that we want to minimise the mean cost of missing deadlines by soft tasks. First, we show that the dynamics of such a system can be modelled as a finite Markov Decision Process (MDP). Second, we show that our scheduling problem is PP-hard and in EXPTime. Third, we report on a prototype tool that solves our scheduling problem by relying on the Storm tool to analyse the corresponding MDP. We show how antichain techniques can be used as a potential heuristic.

Subject Classification

ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Computer systems organization → Real-time system specification
  • Computer systems organization → Embedded systems
  • Non-clairvoyant scheduling
  • hard and soft tasks
  • automatic synthesis
  • Markov decision processes


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