Dynamic activated sludge modeling (ASM) and the concept of chemical oxygen demand fractionation utilized by this modeling approach suggested the existence of new strategies for minimization of excess sludge. One of these strategies consists of eliminating the traditional sludge wastage (WAS) and avoiding the buildup of inert solids in the aeration tanks by other means: fine screens are used to remove the inert particulate organic fraction (X-I), hydrocyclones (HC) are used for inorganic suspended solids (ISS), and different types of online digesters are used to further biodegrade the endogenous residues (X-P) via the return activated sludge (RAS) line. In this research, a model and a simulation program were developed that were able to mimic the apparent behavior of activated sludge variants with low solids production (LSP-AS). The model is an extended ASM1 assuming a small first-order biodegradation constant for X-P (k(Xp) = 0.007 d(-1))(-1)), and black boxes represent X-I and ISS removal. The simulations first depicted the way that different solid components build up in the aeration tanks when traditional activated sludge (C-AS) is operated at very high solids retention times (>100d, without sieves and HC). Secondly, the modeling showed that the C-AS process could hypothetically be replaced by LSP-AS variants with similar levels of active biomass and mixed liquor total suspended solids in the aeration tanks (2,500-3,500mgL(-1) TSS). For the studied case, at least 2 and 6% of the RAS flow must be screened and digested, respectively, to avoid the accumulation of X-I, ISS, and X-P. Additionally, the size of the online digester will be approximately twice the volume of the aeration tank. The mathematical model implemented in Aquasim could serve as a didactical, operational, and research simulation tool for LSP activated sludge processes.