Cloud computing services have significantly increased the potential for organisations and individuals to outsource data storage and computation. A critical concern is how to maintain the confidentiality and the security of data whilst maintaining ease of access and quality of service. This thesis presents an approach for investigating the performance modelling and analysis of management of infrastructure in cloud computing using stochastic process algebra. We investigate the cost of security in cloud computing based on a multi-level security model. Then, explore the use of two tools developed to support the analysis of the stochastic process algebra (PEPA Eclipse Plug-in and GPA) in the context of two models of workflow based systems. These tools are used to examine systems that are concerned with the security matters at the level of IaaS service model, addressed by the Trusted Cloud Computing Platform (TCCP); specifically, examining the performance of the Node Registration protocol and the VM Launch protocol. Next, models are developed to study the performance of two commit protocols the decentralized two phase commit protocol and the decentralized three phase commit protocol. This leads on to an evaluation of the ZooKeeper atomic broadcast protocol Zab, where the broadcast phase of the Zab protocol is formally specified using the Markovian process algebra PEPA. This facilitates a comparison between (2PC, 3PC and ZooKeeper) to find out which of these coordination protocols can provide better performance under different assumptions.