Cloud computing has become an important research area in large-scale computing systems and is being employed by many organizations in government, businesses, and industry. Schemes and appropriate models for dynamic resources provisioning in the cloud environment have been extensively studied. To date, the research literature is lacking schemes and models that offer dynamic scalability in which Quality of Service (QoS) and high performance are provided to customers with the usage of the least number of cloud resources, especially for containerized services hosted on the cloud. With dynamic scalability, cloud computing can offer on-demand, timely, and dynamically adjustable computing resources to services hosted on the cloud. This paper presents a dynamic scaling model based on queueing theory to scale containers virtual resources and satisfy the customer Service Level Agreements (SLA) while guarding costs of scaling very low. The aim is to improve the virtual computing resources utilization and satisfy SLA constraints in terms of CPU utilization, system response time, system drop rate, system number of tasks, and system throughput. Simulation results are provided using Java Modelling Tools simulation tool, which shows that our proposed model can determine under any offered workload the needed containers instances to satisfy the required QoS parameters.

云计算已成为大规模计算系统中的重要研究领域，并已被政府，企业和行业中的许多组织所采用。对云环境中动态资源供应的方案和适当的模型进行了广泛的研究。迄今为止，研究文献缺乏提供动态可扩展性的方案和模型，在这些方案和模型中，使用最少数量的云资源（尤其是对于托管在云中的容器化服务）向客户提供服务质量（QoS）和高性能。凭借动态可伸缩性，云计算可以为托管在云上的服务提供按需，及时且可动态调整的计算资源。本文提出了一种基于排队论的动态扩展模型，用于扩展容器虚拟资源并满足客户服务水平协议（SLA），同时保持非常低的扩展成本。目的是提高虚拟计算资源利用率，并在CPU利用率，系统响应时间，系统丢弃率，系统任务数和系统吞吐量方面满足SLA约束。使用Java Modeling Tools仿真工具提供的仿真结果表明，我们提出的模型可以确定在任何提供的工作负载下满足所需QoS参数的所需容器实例。系统响应时间，系统删除率，系统任务数和系统吞吐量。使用Java Modeling Tools仿真工具提供的仿真结果表明，我们提出的模型可以确定在任何提供的工作负载下满足所需QoS参数的所需容器实例。系统响应时间，系统删除率，系统任务数和系统吞吐量。使用Java Modeling Tools仿真工具提供的仿真结果表明，我们提出的模型可以确定在任何提供的工作负载下满足所需QoS参数的所需容器实例。