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This paper presents a quantitative analysis of an efficient load sharing scheme namely "Dual Layered Load Sharing Scheme (DLLS)" which is highly suitable for large scale distributed systems. The scheme is based on partitioning the system into "independent" clusters called partitions. Load sharing is accomplished at two levels i.e., one within the partition and the other across the partitions. Load sharing within the partition is performed by a variant of a flexible load-sharing algorithm, EFLS, while a utilization rate of partitions is used for the load sharing across the partitions. The primary benefits of decomposing the systems into partitions are better allocations of the tasks to the neighbouring nodes and scalability. The quantitative analysis provides both performance and efficiency measures. NEST simulation tool was used for the implementation and analysis of our DLLS scheme. A detailed comparative study shows a considerable improvement of DLLS over the EFLS under congested communication resources. In particular, it was observed that DLLS achieved a high percentage of close allocation of about 95%, a hit ratio of about 97% and system response time on the average75%.