We present the simulated performance of a Josephson traveling wave parametric amplifier based on a one-dimensional array of radio-frequency single-junction superconducting quantum interference devices. Using the capabilities allowed by the WRspice simulation platform and previous works on this scheme, we include in our study the effects of fabrication tolerances in the device parameters on the gain of the amplifier. Our simulations show the negative effects of parameter variation and the resulting microwave reflections of signal and pump waves between individual cells. We present a method to understand the inner dynamics of the device using an impedance model that substitutes the need to simultaneously consider phase bias points and wave mixing dynamics. This should allow the application of the results presented here to more complex schemes, which promise higher amplification and fewer drawbacks. We highlight the strict limitations on parameter spread in these devices while also discussing the robustness of the scheme to defects.