Developing automotive software is becoming in- creasingly challenging due to continuous increase in its size and complexity. The development challenge is amplified when the industrial requirements dictate extensions to the legacy (previously developed) automotive software while requiring to meet the existing timing requirements. To cope with these challenges, sufficient techniques and tooling to support the modeling and timing analysis of such systems at earlier development phases is needed. Within this context, we focus on the extension of software component chains in the software architectures of automotive legacy systems. Selecting the sampling frequency, i.e. period, for newly added software components is crucial to meet the timing requirements of the chains. The challenges in selecting periods are identified. It is further shown how to automatically assign periods to software components, such that the end-to-end timing requirements are met while the runtime overhead is minimized. An industrial case study is presented that demonstrates the applicability of the proposed solution to industrial problems.