A framework for the quantitative analysis of performance, security and database management within a network system (e.g. a cloud computing platform) is presented within this research. Our study provides a methodology for modelling and quantitatively generating significant metrics needed in the evaluation of a network system. To narrow this research, a study is carried-out into the quantitative modelling and analysis of performance, security and database management trade-offs in cloud computing platforms, based on Stochastic Activity Networks (SANs) and combined metrics. Cloud computing is an innovative distributed computing archetypal based on the infrastructure of the internet providing computational power, application, storage and infrastructure services. Security mechanisms such as: batch rekeying, intrusion detection, encryption/decryption or security protocols come at the expense of performance and computing resources consumption. Furthermore, database management processing also has an adverse effect on performance especially in the presence of big data. Stochastic Activity Networks (SANs) that offer synchronisation, timeliness and parallelism are proposed for the modelling and quantitative evaluations of ‘optimal’ trade-offs involving performance, security and database management. Performance modelling and analysis of computer network systems has mostly been considered of utmost importance. Quantification of performance for a while has been assessed using stochastic models with a rising interest in the quantification of security stochastic modelling being applied to security problems. Quantitative techniques that includes analytical valuations founded on queuing theory, discrete-event simulations and correlated approximations have been utilised in the examination of performance. Security suffers from the point that no interpretations can be made in an optimal case. The most consequential security metrics are in analogy with reliability metrics. The express rate at which data grows increases the prominence for research into the design and development of cloud computing models that manages the workload intensity and are suitable for data exploration. Handling big data especially within cloud computing is a resource consuming, time-demanding and challenging task that necessitates titanic computational infrastructures to endorse successful data exploration. We present an improved Security State Transition Diagram (SSTD) by adding a new security state (Failed/Freeze state). The presence of this new security state signifies a security position of the computing network system were the implemented security countermeasures cannot handle the security attacks and the system fails completely. In a more sophisticated security system, when the security countermeasure(s) cannot in any form categorise the security attack, the network system is moved to the Failed/Freeze security state. At this security state, the network system can only resume operation when restored by the system administrator. In this study, we propose a cloud computing system model, defined security countermeasures and evaluated the optimisation problems for the trade-offs between performance, security and database management using SANs formalism. We designed, modelled and implemented dependency within our presented security system, developing interaction within the security countermeasures using our proposed Security Group Communication System (SGCS). The choice of Petri-Nets enables the understanding and capturing of specified metrics at different stages of the proposed cloud computing model. In this thesis, an overview of cloud computing including its classification and services is presented in conjunction with a review of existing works of literature. Subsequently, a methodology is proposed for the quantitative analysis of our proposed cloud computing model of performance-security-database trade-offs using Möbius simulator. Additionally, numerical experiments with relevant interpretations are presented and appropriate interpretations are made. We identified that there are system parameters that can be used to optimise the presented abstract combined metrics but they are optimal for neither performance or security or database management independently. Founded on the proposed quantitative simulation model framework, reliable numerical experiments were observed and indicated scope for further extensions of this work. For example, the use of Machine Learning (ML) or Artificial Intelligence (AI) in the predictive and prevention aspects of the security systems.