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Development of fast methods to conduct in silico experiments using computational models of cellular signaling is a promising approach toward advances in personalized medicine. However, software-based cellular network simulation has runtimes plagued by wasted CPU cycles and unnecessary processes. Hardware emulation affords substantial speedup, but prior attempts at hardware implementation of biological simulators have been limited in scope and have suffered from inaccuracies due to poor random number generation. In this work, we propose several simulation schemes utilizing novel random update index generation techniques for step-based and round-based stochastic simulations of cellular networks. Our results show improved runtimes while maintaining simulation accuracy compared to software implementations.