Cloud computing has become a growing technology and has received wide acceptance in the scientific community and large organizations like government and industry. Due to the highly complex nature of VM virtualization, lightweight containers have gained wide popularity, and techniques to provision the resources to these containers have drawn researchers towards themselves. The models or algorithms that provide dynamic scalability which meets the demand of high performance and QoS utilizing the minimum number of resources for the containerized cloud have been lacking in the literature. The dynamic scalability facilitates the cloud services in offering timely, on-demand, and computing resources having the characteristic of dynamic adjustment to the end users. The manuscript has presented a technique which has exploited the queuing model to perform the dynamic scalability and scale the virtual resources of the containers while reducing the finances and meeting up the user's Service Level Agreement (SLA). The paper aims in improving the usage of virtual resources and satisfy the SLA requirements in terms of response time, drop rate, system throughput, and the number of containers. The work has been simulated using Cloudsim and has been compared with the existing work and the analysis has shown that the proposed work has performed better.