Zero-Jitter Chains of Periodic LET Tasks via Algebraic Rings

In embedded computing domains, including the automotive industry, complex functionalities are split across multiple tasks that form task chains . These tasks are functionally dependent and communicate partial computations through shared memory slots based on the Logical Execution Time (LET) paradigm. This paper introduces a model that captures the behavior of a producer-consumer pair of tasks in a chain, characterizing the timing of reading and writing events. Using ring algebra, the combined behavior of the pair can be modeled as a single periodic task. The paper also presents a lightweight mechanism to eliminate jitter in an entire chain of any size, resulting in a single periodic LET task with zero jitter. All presented methods are available in a public repository.