Network Function Virtualisation (NFV) has been considered as a promising technology for future Internet to increase network flexibility, accelerate service innovation and reduce the Capital Expenditures (CAPEX) and Operational Expenditures (OPEX) costs, through migrating network functions from dedicated network devices to commodity hardware. Recent studies reveal that although this migration of network function brings the network operation unprecedented flexibility and controllability, NFV-based architecture suffers from serious performance degradation compared with traditional service provisioning on dedicated devices. In order to achieve a comprehensive understanding of the service provisioning capability of NFV, this paper proposes a novel analytical model based on Stochastic Network Calculus (SNC) to quantitatively investigate the end-to-end performance bound of NFV networks. To capture the dynamic and on-demand NFV features, both the non-bursty traffic, e.g. Poisson process, and the bursty traffic, e.g. Markov Modulated Poisson Process (MMPP), are jointly considered in the developed model to characterise the arriving traffic. To address the challenges of resource competition and end-to-end NFV chaining, the property of convolution associativity and leftover service technologies of SNC are exploited to calculate the available resources of Virtual Network Function (VNF) nodes in the presence of multiple competing traffic, and transfer the complex NFV chain into an equivalent system for performance derivation and analysis. Both the numerical analysis and extensive simulation experiments are conducted to validate the accuracy of the proposed analytical model. Results demonstrate that the analytical performance metrics match well with those obtained from the simulation experiments and numerical analysis. In addition, the developed model is used as a practical and cost-effective tool to investigate the strategies of the service chain design and resource allocations in NFV networks.