Schedulability Analysis of Malleable Tasks with Arbitrary Parallel Structure

Multiprocessor systems are increasingly being used in real-time computing, and much research has been done on schedulability analysis of these systems. However, current schedulability analyses have only limited support for joblevel parallelism (JLP): jobs are typically restricted to a simple parallel structure, and malleable jobs, where the number of processors assigned to a job is dynamic, is not widely supported. This paper presents a framework for analyzing systems with malleable jobs of an arbitrary parallel structure. A fair intra-job scheduler is assumed, allowing the state of a job to be represented by a scalar and its parallel structure to be modeled as a function. It is demonstrated that jobs executing their worst-case computations do not necessarily constitute a worst-case scenario with respect to schedulability. This implies that exact schedulability analysis will not be sustainable. Upper bounds on interference and demand are developed. This framework is then used to construct a pessimistic, but sustainable schedulability test for systems scheduled with EDF. The EDF test has poor worst-case performance, but does allow schedulability analysis for a class of systems for which no other analysis currently exists. We believe the framework itself could also be used to construct analyses with better performance.