Grid scheduling is the process of making scheduling decisions involving resources over multiple domains. This process can include searching multiple administrative domains to use a single machine or scheduling a single job to use multiple resources at a single site or multiple sites. In an increasing number of scientific disciplines the enormous potential of the grid can be realized with the fundamental development of potential new scheduling techniques. Conventional scheduling techniques are queue based and provide only one level of service. In this paper we propose an algorithm for effective scheduling of jobs by the local scheduler considering the virtual time and proportional fairness to have a high rate of accuracy and low overhead. We describe the various scheduling algorithms that are in use and next, we explain the virtual time fair queuing algorithm with its implementation and the results. © 2009 Springer.