Grid computing systems utilize distributively owned and geographically dispersed resources for providing a wide variety of services for various applications. One of the key considerations in Grid computing systems is resource management with quality of service constraints. The quality of service constraints dictate that submitted tasks should be completed by the Grid in a timely fashion while delivering at least a certain level of service for the duration of execution. Because t e Grid is a highly "dynamic" system due to the arrival and departure of tasks and resources, it is necessary to perform advance reservations of resources to ensure their availability, and to meet the requirements of the different tasks. This thesis introduces two new scheduling algorithms for advance reservations including co-reservations, namely, 'Reservation Scheduler with Priorities and Benefit Functions' (RSPB) and 'Co-Reservation Scheduler with Priorities and Benefit Functions' (Co-RSPB). The algorithms consider the relative priorities of various reservation requests while scheduling reservations. The benefit function is used to quantify the "profit" for the client in order to remove the re-negotiation overhead in case of resource scarcity. Simulations are performed to compare proposed algorithms with an existing approach or with some comparison algorithms developed as basic comparison line in this thesis. The results indicate that the proposed algorithms can improve the overall the performance by satisfying larger number of reservation requests.