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<p><it>Abstract—</it>Most existing analytical models for memory interference generally assume random bank selection for each memory access. In vector computers, however, memory accesses are typically regularly patterned with a number of data items being accessed concurrently from different banks. Very little is known about the queueing behavior of memory interferences in multiple stream vector accesses. This paper presents an analytical model for memory interferences due to vector accesses in multiple vector processor systems. The model captures the effects of both bank conflicts among elements within one vector access stream and conflicts among multiple vector access streams on system performance. The model is based on a closed queueing network assuming an ideal interconnection network. An approximation technique is proposed to solve the memory queueing system that serves customers in a complicated way (non-FIFO). We also carry out extensive simulation experiments to study memory interference and validate our analytical model. Simulation results and analytical results are in a very good agreement, indicating that the model is very accurate. We further validate our analysis by comparing the numerical results obtained from our analytical model with those measurement results that were published by other researchers. Based on our analytical model and simulations, we carry out performance evaluation of the multiple vector processor systems. Our numerical results show that memory access conflicts pose a severe limitation on the number of useful processors in the system, implying that memory system design is essential to high-performance computing.</p>

Q. Yang and T. Yang, "A Memory Interference Model for Regularly Patterned Multiple Stream Vector Accesses," in IEEE Transactions on Parallel & Distributed Systems, vol. 6, no. , pp. 520-530, 1995.
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