Markov Chain Model Using Lévy Flight for VLSI Power Grid Analysis

Due to complex architectures of modern high performance processor designs, signal integrity across the power grid network has become a challenging issue. To ensure reliable signal delivery, the process of power grid analysis requires definite investigation of entire power grid network for any hotspot (worst-case voltage fluctuation) using efficient algorithms during chip design and verification. As the process is inherently iterative and considering the size of modern chips, it requires extensive computations to locate the hotspots across the power grid network. This enables to employ correct methodology to efficiently analyze large power grid networks in suitable computing environment. This paper presents a method based on Markov chain algorithm model, which utilizes a Levy flight principle to identify the region of influence, i.e. hotspots of a power grid network using graphics processing units (GPUs). Here, the basic idea of proposed method is to traverse the power grid network depending upon the states acquired in each step during transition on Markov chain using Levy flight. Experimental results show that the proposed method demonstrates remarkable performance improvement over state-of-art solutions with acceptable accuracy loss (≤ 4%). Further, a speedup of 2.48× has been achieved over serial version of proposed method on GPU while analyzing a power grid network having 49 million vertices.