Paper Title
A Closed-Form Solution for Deadline-Based Scheduling Divisible Load in Distributed Systems

Abstract
The interest and importance of load scheduling in distributed systems have grown considerably in the past decade. Divisible load Theory (DLT) merged as a powerful analytical tool to allocate the load in distributed systems. There are hundreds of articles based on DLT. Deadline-Based Scheduling Algorithm (DBSA) proposed a method, for the first time, to divide and distribute the load based on resources deadline, not task deadline, in homogenous distributed systems. All analysis in DLT assumes all nodes (processors) system is available during the execution time of the divisible task. DBSA considers, for the first time, the available time of each node participating in executing the divisible task. DBSA was developed to homogenous environment. It is not easy to extend it to the heterogeneous distributed systems; this is the Major problem in DBSA. Our work is taking The DBSA one step further. We propose an analytical solution for distributing the load in homogenous distributed systems as a one-step replacement for the DBSA. The one-step analytical solution has far much less complexity comparing to the O(n) complexity of DBSA. Our solution paved the way to obtain a solution for more realistic heterogeneous distributed grid systems. Of course, this will open a new dimension of research where we can complicate the distributed systems to resemble real time complex distributed systems. Working with heterogonous environment requires finding the optimal processors sequence for load distribution; this is another dimension for future research. The proposed analytical enabled us, easily, to investigate the effect of different system parameters, which affects scheduling, on the optimal finish time; a tool that is very important for system engineers to tune the system parameters. The results of the derived equations were compared with previous results and shown to be precisely the same. Index Terms— Divisible Load Theory, Distributed Systems,