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Self-adaptive software (SAS) is gaining in popularity as it can handle dynamic changes in the operational context or in itself. Time behaviors are of vital importance for SAS systems, as the self-adaptation loops bring in additional overhead time. However, early modeling and quantitative analysis of time behaviors for the SAS systems is challenging, especially under uncertainty environments. To tackle this problem, this paper proposed an approach called Timed-SAS to define, describe, analyze, and optimize the time behaviors within the SAS systems. Concretely, Timed-SAS: (1) provides a systematic definition on the deterministic time constraints, the uncertainty delay time constraints, and the time-based evaluation metrics for the SAS systems; (2) creates a set of formal modeling templates for the self-adaptation processes, the time behaviors and the uncertainty environment to consolidate design knowledge for reuse; and (3) provides a set of statistical model checking-based quantitative analysis templates to analyze and verify the self-adaptation properties and the time properties under uncertainty. To validate its effectiveness, we presented an example application and a subject-based experiment. The results demonstrated that the Timed-SAS approach can effectively reduce modeling and verification difficulties of the time behaviors, and can help to optimize the self-adaptation logic. |
