Utilizing non-zero offsets when scheduling real-time periodic processes significantly increases the chances of satisfying all the timing constraints in a real-time system. In this paper, a method that enables the utilization of non-zero offsets in the pre-run-time scheduling of asynchronous and periodic processes with release times, deadlines, precedence and exclusion relations on either a uniprocessor or on a multiprocessor in real-time embedded systems is presented. This paper also identifies for the first time, the set of general conditions that a periodic process newpi with release time rnewpi, computation time cnewpi, deadline dnewpi, period prdnewpi, permitted range of offset onewpi, must satisfy, in order to satisfy the timing constraints of any given asynchronous process ai with computation time cai, deadline dai, minimum time between two consecutive requests minai, and earliest time that asynchronous process ai can make a request for execution lai. A method based on these general conditions for converting asynchronous processes with earliest request times into new periodic processes with offset constraints is also introduced.

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