Citation: Han, D.; Cai, Y.; Chen, W.;
Cui, Z.; Li, A. Timed-SAS: Modeling
and Analyzing the Time Behaviors of
Self-Adaptive Software under
Uncertainty. Appl. Sci. 2023, 13, 2018.
https://doi.org/10.3390/
app13032018
Academic Editors: Sanjay Misra,
Robertas Damaševiˇcius and
Bharti Suri
Received: 21 November 2022
Revised: 29 January 2023
Accepted: 30 January 2023
Published: 3 February 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Timed-SAS: Modeling and Analyzing the Time Behaviors of
Self-Adaptive Software under Uncertainty
Deshuai Han
1,
* , Yanping Cai
1
, WenJie Chen
2
, Zhigao Cui
1
and Aihua Li
1
1
College of Defense Engineering, Rocket Force University of Engineering, Xi’an 710025, China
2
College of Defense Engineering, Army Engineering University of PLA, Nanjing 210007, China
* Correspondence: handeshuai@126.com
Featured Application: The Timed-SAS approach can be used to design and quantitatively analyze
the complex self-adaptive software systems, such as cloud computing systems.
Abstract:
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 quanti-
tative 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.
Keywords:
self-adaptive software; time behavior; formal modeling; quantitative analysis; formal
templates
1. Introduction
Nowadays, complex software systems such as the cloud computing systems [
1
] and
the cyber-physical systems [
2
] are facing new challenges due to increasing size, incremental
complexity, and unpredictable environment changes. While addressing these challenges,
it becomes necessary to develop self-adaptive software (SAS) [
3
]. In fact, software self-
adaptation has become a research hot topic [
4
,
5
] in the software engineering community.
Self-adaptation endows a software system with the capability to satisfy certain objectives
by automatically modifying its parameters, structures, or behaviors, with the commonly
used MAPE-K (Monitor-Analyze-Plan-Execute, Knowledge) self-adaptation loops [6].
SAS systems run in dynamic and uncertainty environments, and it is necessary to
provide rigorous evidence to guarantee that the self-adaptation processes, time behaviors,
and properties are correct and satisfied through particular formal models, such as the
automaton model [
7
] and Petri-nets model [
8
], as discussed in “Assurances for Self-Adaptive
Systems” [
9
]. The network of timed automata (NTA) seems to be a promising formal model
to specify system behaviors for the SAS systems, and many research studies, such as the
ActivFORMS method [
10
], the MAPE-K formal templates [
11
], and the eARF reasoning
framework [
12
], attempted to formally specify the SAS systems with the NTA model.
Appl. Sci. 2023, 13, 2018. https://doi.org/10.3390/app13032018 https://www.mdpi.com/journal/applsci
