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Multi-core processor architectures are gaining huge interests from academia and industry. The multi-core architectures have been proposed and designed for overcoming diminishing return and for efficiently utilizing the exponentially increasing number of transistors available in nano-meter semiconductor technology. Though the multi-core architecture has been proposed as a promising alternative to a traditional monolithic core architecture, performance characteristics and benefits of the multi-core architecture are not well studied. In this paper, we develop an asymptotic analysis model for better understanding the performance characteristics of multi-core processor architectures using Amdahl's law in order to foresee their performance impact for a given workload characteristics (e.g. available parallelism). Through the asymptotic analysis based on the models proposed in this paper, we can make the architectural design decisions such as Â¿the number of coresÂ¿ and Â¿core sizeÂ¿, and further we can probe the possible research direction of optimizing the performance of multi-core architectures.