CCTV cameras produce a large amount of video surveillance data per day, and analysing them require the use of significant computing resources that often need to be scalable. The emergence of the Hadoop distributed processing framework has had a significant impact on various data intensive applications as the distributed computed based processing enables an increase of the processing capability of applications it serves. Hadoop is an open source implementation of the MapReduce programming model. It automates the operation of creating tasks for each function, distribute data, parallelize executions and handles machine failures that reliefs users from the complexity of having to manage the underlying processing and only focus on building their application. It is noted that in a practical deployment the challenge of Hadoop based architecture is that it requires several scalable machines for effective processing, which in turn adds hardware investment cost to the infrastructure. Although using a cloud infrastructure offers scalable and elastic utilization of resources where users can scale up or scale down the number of Virtual Machines (VM) upon requirements, a user such as a CCTV system operator intending to use a public cloud would aspire to know what cloud resources (i.e. number of VMs) need to be deployed so that the processing can be done in the fastest (or within a known time constraint) and the most cost effective manner. Often such resources will also have to satisfy practical, procedural and legal requirements. The capability to model a distributed processing architecture where the resource requirements can be effectively and optimally predicted will thus be a useful tool, if available. In literature there is no clear and comprehensive modelling framework that provides proactive resource allocation mechanisms to satisfy a user's target requirements, especially for a processing intensive application such as video analytic. In this thesis, with the hope of closing the above research gap, novel research is first initiated by understanding the current legal practices and requirements of implementing video surveillance system within a distributed processing and data storage environment, since the legal validity of data gathered or processed within such a system is vital for a distributed system's applicability in such domains. Subsequently the thesis presents a comprehensive framework for the performance ii modelling and optimization of resource allocation in deploying a scalable distributed video analytic application in a Hadoop based framework, running on virtualized cluster of machines. The proposed modelling framework investigates the use of several machine learning algorithms such as, decision trees (M5P, RepTree), Linear Regression, Multi Layer Perceptron(MLP) and the Ensemble Classifier Bagging model, to model and predict the execution time of video analytic jobs, based on infrastructure level as well as job level parameters. Further in order to propose a novel framework for the allocate resources under constraints to obtain optimal performance in terms of job execution time, we propose a Genetic Algorithms (GAs) based optimization technique. Experimental results are provided to demonstrate the proposed framework's capability to successfully predict the job execution time of a given video analytic task based on infrastructure and input data related parameters and its ability determine the minimum job execution time, given constraints of these parameters. Given the above, the thesis contributes to the state-of-art in distributed video analytics, design, implementation, performance analysis and optimisation.