Abstract
In recent years, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">time-triggered</i> communication protocols have been developed to support time-critical applications for in-vehicle communication. In this respect, the FlexRay protocol is likely to become the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">facto</i> standard. In this paper, we investigate the scheduling problem of periodic signals in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">static</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">segment</i> of FlexRay. We identify and solve two subproblems and introduce associated performance metrics: (1) The signals have to be packed into equal-size messages to obey the restrictions of the FlexRay protocol, while using as little bandwidth as possible. To this end, we formulate a nonlinear integer programming (NIP) problem to maximize bandwidth <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">utilization</i> . Furthermore, we employ the restrictions of the FlexRay protocol to decompose the NIP and compute the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimal</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">message</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">set</i> efficiently. (2) A message schedule has to be determined such that the periodic messages are transmitted with minimum <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">jitter</i> . For this purpose, we propose an appropriate software architecture and derive an integer linear programming (ILP) problem that both minimizes the jitter and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bandwidth</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">allocation</i> . A case study based on a benchmark signal set illustrates our results.
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