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The resistive random access memory (RRAM) crossbar array has been extensively studied as one of the most promising candidates for future high-density nonvolatile memory technology. However, some problems caused by circuit and device interaction, such as sneak leakage paths, result in limited array size and large power consumption, which degrade the array performance significantly. Thus, the analysis on circuit and device interaction issue is imperative. In this paper, a simulation method is developed to investigate the critical issues correlated with the interaction between devices and the circuit. The simulations show that a large off/on ratio of resistance states of RRAM is beneficial for large readout margin (i.e., array size). The existence of the selector connected in series with an RRAM device can eliminate the need for high Ron resistance, which is critical for the array consisted of only RRAM cells. The readout margin is more sensitive to the variation of Ron and is determined by the nonlinearity of the I-V characteristics of RRAM, whereas the nonlinear characteristics of the selector device are beneficial for a larger readout margin. An optimal design scheme for turn-on voltage and conductance of the selector is proposed based on the simulation.