Size-based load distribution approaches are proposed to deal with high variation of task size. One of the most critical problem of these approaches is that they do not consider task deadlines (which if not met may cause task starvation). This paper proposes an extension of our early work on dynamic load balancing [8, 7, 2] (called LFF) which takes the relative processing time of a task into account and dynamically assigns it to the fittest server with a lighter load and higher processing capacity. LFF-PRIORITY dynamically computes the task size priority and task deadline priority and puts them in a priority based multi-section queue. The testing results clearly show that LFF-PRIORITY out performs existing load distribution strategies. More importantly, more than 80% of tasks meet their task deadlines under LFF-PRIORITY strategy.