ELSEVIER Information Processing Letters 53 (1995) 249-254 Information Processing Letters Optimal priority assignment for aperiodic tasks with firm deadlines in fixed priority pre-emptive systems Robert Davis *, Alan Burns zyxwvutsrqponmlkjihgfedcbaZYXWVU Real-Time Systems Research Group, Department of Computer Science, University of York, York YOI SDD, United Kmgdom Communicated by R.S. Bird; received 8 August 1994; revised 21 October 1994 Abstract An optimal priority assignment policy is presented for independent aperiodic tasks with arbitrary ready times and firm deadlines, scheduled on a uniprocessor along with a set of hard periodic/sporadic tasks. The latter tasks are assumed to have been assigned unique fixed priorities according to some arbitrary policy and guaranteed, via off-line feasibility analysis, to meet their deadlines. In contrast, priority assignment and acceptance testing of aperiodic tasks must be carried out on-line. The priority assignment policy introduced is shown to be optimal both in terms of maximising the computation time which can be made available before the aperiodic deadline and with respect to guaranteeing subsequent aperiodic arrivals. Keywords: Real-time; Scheduling; Algorithms; Priority assignment 1. Introduction In this paper, we discuss the priority assign- ment and acceptance testing of aperiodic tasks with firm deadlines. We introduce an optimal priority assignment policy which maximises the computation time which can be made available by the aperiodic deadline, given a set of previously guaranteed hard periodic/ sporadic tasks. Research into on-line acceptance tests has been carried out by Chetto and Chetto [lo], Schwan and Zhou [9] and Kim [4] with respect to earliest deadline scheduling. However, when ap- plied to the case of mixed task sets, (aperiodic * Corresponding author. Email: robd@minster.york.ac.uk. and periodic) the tests presented in [lo] and [9] are pseudo-polynominal in complexity: in the worst case the time taken to perform the tests depends upon the number of task invocations within the least common multiple (LCM) of the hard task periods. Further, the model used by Schwan and Zhou requires that all task invoca- tions, both periodic and aperiodic, undergo an on-line acceptance test, leading to unnecessarily high overheads. The test presented by Kim also requires that all task invocations undergo accep- tance testing. However, of greater consequence, is the implicit assumption that tasks with an ear- lier ready time are of greater importance, and are therefore accepted in preference to, those with a later ready time. When mixed task sets are con- sidered, this assumption no longer holds and it is 0020-0190/95/$09.50 0 1995 Elsevier Science B.V. AI1 rights reserved XSDZ 0020-0190(94)00200-2