We present algorithms for the scheduling sequential tasks on a Network Enabled Server (NES) environment. We have implemented the non-preemptive scheduling, since at the user level we cannot interrupt a running process and block it in order to allow a new process to run. This article is an extension of the paper: "A Study of Deadline Scheduling for Client-Server Systems on the Computational Grid" by Takefusa et al. We mainly discuss a deadline scheduling with priority strategy that is more appropriate for multi-client, multi-server case. Importance is first given to the task's priority and then the task is allocated to the server that can meet the task's deadline. This may cause that some already allocated tasks on the server miss their deadline. We augment the benefits of scheduling algorithms with load measurements (which is done with the use of a forecasting tool called FAST) and fallback mechanisms. The experimental results shows that the deadline scheduling with priority along with fallback mechanism can increase the overall number of tasks executed by the NES.