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So far, performance prediction and optimization of microwave SQUID multiplexers has largely been based on simple approximate analytical models and experimental results. This is caused by the complexity of the underlying physics and the intricacy of operation and readout parameters. As a simplified description can never account for all potential effects occurring in a real device, we have developed a software framework to simulate the characteristics and performance of a microwave SQUID multiplexer. Our simulation framework is a powerful tool to guide understanding and optimization of microwave SQUID multiplexers and other related devices. It includes common readout schemes such as open-loop or flux ramp modulated readout as well as the nonlinear behavior of Josephson tunnel junctions. Moreover, it accounts for the non-zero response time of superconducting microwave resonators with high loaded quality factors as well as the most significant noise contributions such as amplifier noise, resonator noise as well as SQUID noise. This ultimately leads to a prediction of device performance that is significantly better as compared simple analytical methods. Using the simulation framework, we discuss first steps towards a full microwave SQUID multiplexer optimization and highlight some other applications which our simulation framework can be used for.