The ammonia-water absorption refrigeration system is attracting increasing research interests, since the system can be powered by waste thermal energy, thus avoiding using ozone-depletion refrigerants and reducing demand on electricity supply. In the article, a mathematical model coupled with detailed equations for thermodynamic properties of an ammonia-water mixture is described A computer simulation software based on the model is developed. With the software, the performance characteristics of ammonia-water absorption refrigeration systems are analyzed, and detailed optimum operation maps for the systems are presented. These maps can be used as guides in choosing operating conditions for designing such systems or for existing systems.