Analysis of Divisible Load Scheduling with result collection on HETerogeneous Systems

Divisible Load Theory (DLT) is an established framework to study Divisible Load Scheduling (DLS). Traditional DLT ignores the result collection phase, and specifies no solution to the general case where both the network speed and computing capacity of the nodes are heterogeneous. In this paper, the DLS with Result Collection on HETerogeneous Systems (DLSRCHETS) problem is formulated as a linear program and analyzed. The papers to date that have dealt with result collection, proposed simplistic LIFO (Last In, First Out) and FIFO (First In, First Out) type of schedules as solutions. The main contributions of this paper are: (a) A proof of the Allocation Precedence Condition, which is inconsequential in LIFO or FIFO, but is important in a general schedule. (b) A proof of the Idle Time Theorem, which states that irrespective of whether load is allocated to all available processors, in the optimal solution to the DLSRCHETS problem, at the most one processor that is allocated load has idle time, and that the idle time exists only when the result collection begins immediately after the completion of load distribution.