Analytical results on the real-time scheduling of multiprocessor systems have focused on partitioning and distributing the task set for scheduling on identical single processors, with the assumption that all of a task can be executed on any of a pool of identical processors. A distributed system is a set of nodes networked together. Each node may have a different type of processor and performs different functions. In the distributed environment, a real-time task may require processing on multiple nodes. However, all the nodes have to satisfy the time constraints of the task. In this paper, we show that the Liu & Layland (1973) type of classical task models must be extended to handle this type of distributed real-time tasks. We propose a distributed generalized multi-frame (DGMF) task model. The scheduling problem of DGMF tasks can be reduced to that of scheduling generalized multi-frame (GMF) tasks on a single processor. We analyze the fixed-priority scheduling of (D)GMF tasks and prove that the deadline-monotonic priority assignment is not optimal for the general case of frame-wise priority assignment. In the context of relative deadline assignment, we show that there are simple cases for which deadline-monotonic assignment is optimal.
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