Desktop grid systems are one of the largest paradigms of distributed computing in the world. The idea is to use the idle and underutilized processing cycles and memory of the desktop machines to support large scale computation. The design issues in desktop grid systems are much more complex as compared to traditional grid environment because the hosts (desktop machines) participating in the computation do not work under one administrative control and can become unavailable at any point in time. The heterogeneity and volatility of computing resources, for example, diversity of memory, processors, and hardware architectures also play its role. To get fruitful results from such hostile environment, scheduling tasks to better hosts become one of the most important issues. The thesis focuses on the issue of task scheduling and resource allocation in desktop grid systems and presents concrete contributions in two separate areas. The first contribution of the thesis is about minimizing the applications turnaround time on desktop grid systems that can only be achieved through knowledgeable task scheduling mechanism. A Group based Fault Tolerant Scheduling and Replication Mechanism (labeled as GFTSRM) is proposed that uses collective impact of CPU and RAM, task completion history and spot checking to populate available hosts in relevant groups to perform group based task scheduling. It is shown that grouping the hosts on the basis of computing strength and behavior is necessary for better performance. Relevant replication strategies are appended to each group in order to reduce the wastage of processing cycles. Simulations are performed by using GFTSRM, FCFS (First Come First Serve) and PRI-CR-Excl (host exclusion based on the fixed threshold of clock rate). GFTSRM is compared with FCFS because it is the most commonly used task scheduling mechanism. PRI-CR-Excl is used for comparison with the proposed group based scheduling mechanism that takes into account “collective impact of CPU and RAM” while on the contrary PRI-CR-Excl excludes hosts on the fixed threshold of clock rate. The simulation results show that GFTSRM reduces the application turnaround time by more than 35% as compared to FCFS. The proposed group based scheduling mechanism also depicted improvement of more than 20% on application completion time as compared to PRI-CR-Excl. The second contribution of the thesis is about predicting the host availability in desktop grid systems by using Predictive Analytics (PA) that can help in scheduling tasks to highly available hosts. A comprehensive, high-level evaluation of standard PA techniques to predict host availability in desktop grids is presented with the aim to determine the relatively better algorithms. This work goes a step-ahead than related work in which researchers have applied a single PA approach to a standard desktop grid setting. The work addressed both PA perspectives, i.e., classification and regression and used the following standard classification algorithms: k-Nearest Neighbour (k-NN) for Lazy Learning technique, Naïve Bayes for Bayesian learning technique, LibSVM library for Support Vector Modeling (SVM) technique, Random Forest for Tree Induction technique, and Multi-Layer Perceptron (MLP) for Neural Network technique. It is found that the level of selected threshold for availability is critical for acquiring accurate predictions, and k-NN gives the best accuracy across all thresholds. Also, precision-wise, SVM gives perfect performance (100%) across all thresholds followed closely by Neural Networks. Multiple Linear Regression (MLR), Polynomial Regression (PR) and MLP are used for regression, and it is found that MLP gives the best performance, followed by PR and MLR.