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A NUMA system has 50 nodes. Each node is a machine with 4 cores and 4GB memory. 2GB is allotted by OS for dynamic memory allocation per machine. Average local memory access time is 5ns and average remote memory access time is 50ns. A parallel program P needs to process 40GB information. Entire information is pre-loaded into dynamic memories of different nodes of this NUMA system. During execution of P, 10 nodes has been allotted with exclusive access to entire 2GB dynamic memory space. Each sub-process of P is processing equal amount of information. Each process is executing 100 million instructions(all the instructions are local memory access)

a. If each instruction takes 5ns to complete excluding time for instruction memory read and data memory access, what is the total time to complete processing 40GB information in sec?

b. If OS would have allotted 3GB dynamic memory allocation per machine, what would be speed up in new configuration?

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