Attribute Assignment for the Integration of Off-line and Fixed Priority Scheduling Radu Dobrin and Gerhard Fohler Department of Computer Engineering M¨ alardalen University, Sweden radu.dobrin,gerhard.fohler @mdh.se Abstract In this paper we present work to combine fixed priority scheduling with off-line schedule construction. It assumes a schedule has been constructed off-line for a set of tasks to meet their complex constraints. Our method takes the schedule and assigns the FPS attributes priority, offset, and period, to the tasks, such that their runtime FPS execution matches the off-line schedule. It does so by dividing the schedule into sequences and deriving priority inequalities, which are then resolved by integer linear programming. As FPS cannot reconstruct all schedules with periodic tasks, we have to split tasks into several instances to achieve con- sistent task attributes. Our algorithm constructs the mini- mum number of such artifact tasks. 1 Introduction Off-line scheduling and fixed priority (FPS) scheduling are often considered as having incompatible paradigms, but complementing properties: off-line scheduling provides for predictability, distribution, and complex constraints such as jitter or end-to-end deadlines, but no runtime flexibility. FPS, on the other hand, provides this flexibility, but is lim- ited to simple constraints, such as mutual exclusion. In this paper, we present work to combine FPS with off- line schedule construction. It assumes a schedule has been constructed off-line for a set of tasks to meet their complex constraints. Our method takes the schedule and assigns the FPS attributes, priority, offset, and period, to the tasks, such that their runtime FPS execution matches the off-line sched- ule. It does so by dividing the schedule into sequences and deriving priority inequalities, which are then resolved by in- teger linear programming. Thus, our method combines FPS flexibility at runtime with the capability of off-line schedul- ing to resolve complex constrained tasks. FPS cannot reconstruct all schedules with periodic tasks with same priorities for all instances directly. The con- straints expressed via the off-line schedule may require dif- ferent task sequences for instances of the same tasks, as, e.g., by earliest deadline first, leading to inconsistent pri- ority assignment, which can be expressed as a circle of in- equalities. Our algorithm detects such situations, and circumvents the problem by splitting a task into its instances, which are treated as tasks, and assigning different priorities to the newly generated “artifact” tasks, the formerly conflicting instances. A key issue in resolving the priority conflicts is the num- ber of artifact tasks created. Depending on where a priority conflict circle is “broken”, the number may vary, depending on the periods of the split tasks. Our algorithm constructs the minimum number of such artifact tasks. Priority assignment for FPS tasks has been studied in, e.g., [1], [4], and [5] study the derivation of task attributes to meet a overall constraints, e.g., demanded by control per- formance. Instead of specific requirements, our algorithm takes an entire off-line schedule and all task requirements to determine task attributes. A method to transform off- line schedules into earliest deadline first tasks has been pre- sented in [3]. A related paper [2] deals with priority as- signment for offline schedules, but using only a construc- tive, heuristic approach, potentially creating large numbers of artifacts tasks. 2 Algorithm Figure 1 gives an overview of the algorithm. 2.1 Overview 1) Initially, tasks are given with their original constraints, and attributes, including worst case computation times, and periods. 2) A standard off-line scheduling-algorithm constructs off-line scheduling tables with (1) as input.