Clouds are complex systems that provide computing resources in an elastic way. Elasticity allows their adaptation to input workloads by (de)provisioning resources as the demand rises and drops. Given the numerous overlapping factors that impact their elasticity and the unpredictable nature of the workload, providing accurate action plans to manage Cloud elasticity is a particularly challenging task. In this paper, we propose a formal approach based on bigraphical reactive systems to model Cloud structures and their elastic behavior. We design cross-layer elasticity strategies which operate at application and infrastructure Cloud layers to manage the elastic adaptations. We encode the elastic behaviors in Rewriting logic, through the Maude framework, to enable their generic executability. We provide a qualitative verification of the designed behaviors’ correctness with a model-checking technique supported by the linear temporal logic. Finally, we provide a tooled simulation-based methodology, through the Queuing theory, to conduct a quantitative analysis of the designed elasticity strategies.

云是复杂的系统，以弹性方式提供计算资源。弹性允许它们随着需求的上升和下降通过（取消）配置资源来适应输入的工作负载。鉴于许多重叠的因素会影响其弹性以及工作负载的不可预测性，因此提供准确的行动计划来管理云弹性是一项特别具有挑战性的任务。在本文中，我们提出了一种基于传记式反应系统的正式方法来对云结构及其弹性行为进行建模。我们设计跨层弹性策略，该策略在应用程序和基础架构云层上运行，以管理弹性适应。我们通过Maude框架在Rewrite逻辑中对弹性行为进行编码，以实现其通用的可执行性。我们使用线性时间逻辑支持的模型检查技术对设计行为的正确性进行定性验证。最后，我们通过排队理论提供了一种基于工具的基于仿真的方法，对设计的弹性策略进行了定量分析。