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.