Do any of the following:

• Use single-sided instead of double-sided surfaces (which is the default) on the object’s Attribute Editor. The biggest speed gain is for the Maya hardware renderer.
• Tessellating large surfaces requires a lot of memory, so use several small surfaces instead of one large surface when you can. The renderer is more efficient with smaller surfaces.
• For Maya software rendering and Maya hardware rendering, use bump mapping instead of displacement mapping.
• For Maya software rendering, make bump maps flatter. To do this, reduce the value of the Alpha Gain attribute, which smooths the bump map and reduces the number of samples of adaptive shading. This technique only works when Edge Anti-aliasing is set to Highest Quality. The texture bump looks flatter when the Alpha Gain is lower.
• For Maya software rendering, turn on Use Displacement Bounding Box when using displacement maps.
• For Maya software rendering, use layered textures when possible, instead of a Layered Shader. (See Layered shaders and 2D and 3D textures for details.)
• For Maya software rendering and mental ray for Maya, if you are raytracing the scene, set the Reflection Limit and Refraction Limit to the lowest values that produce acceptable results.
• For Maya software rendering, in the Render Settings: Maya Software tab on Linux, Use File Cache avoids re-tessellation of the same surface during rendering. Turn on Use File Cache to store geometric data in a separate file in a location that you specify (the default location is /usr/tmp, but you can set a new location by typing setenv TMPDIR xxx, where xxx is the name of the directory where this file is output).