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In this paper we present a novel load distribution strategy for scheduling divisible loads on linear networks, when the speeds of the computing nodes and the speeds of the communication links are unknown. This practical assumption is captured in our problem formulation and we present a novel strategy, referred to as Early Start Strategy (ESS), to generate a load distribution. Our strategy estimates the speed parameters and takes distinct advantage in utilizing a processor that responds earliest in the computation and including other fast processors in a progressive manner in phases to minimize the overall processing time. We analyze the strategy under several influencing parameters such as, load size, network size, and probe load size. We present simulation studies to validate all the theoretical cal findings and quantify the performance of our strategy.