Although cloud service providers have deployed numerous large-scale cloud data centres world-wide, research in performance modelling for cloud data centres are still in its infancy. A precise model of a cloud data centre can help the service providers improve their service quality, capacity planning, load balance and reduce operation costs. Most studies in literature focused on modelling hypervisor based cloud, typically IaaS. With the growing popularity of containers in cloud service providers; there is a need to develop performance models specifically for these systems. In this paper, a novel cloud analytic model (CAM) for container-based cloud data centre was proposed. The interactive stochastic models are used to analyse the performance of the system in terms of mean job delay and probability of job rejection. Finally, a container emulation framework, ConSim, was developed and tested against the analytic model. Experimental development using real data were compared with theoretical calculation.