We present a modified version of the time-marching algorithm (TMA) [van Ruymbeke et al., 2005, 2010] for predicting the linear viscoelasticity of monodisperse symmetric star polymer melts. Several new elements were added to the original TMA model. In particular, the remaining fraction of the initial tube segments is considered as a function of time, while taking into account the past relaxation history of each molecular segment. We validate the TMA model and, for the first time, compare it with the so-called BoB model [Das et al., 2006]. The predictions obtained with the two models are compared to a large set of experimental data, which cover a broad range of arm molecular weights (from 1.5 to 55 entanglements per arm) of different chemistries (polystyrene, polybutadiene, and polyisoprene). We indicate the significant differences between the two approaches, which mainly affect the choice of material parameters of the models. We then point out a systematic deviation of the TMA model in accurately predicting the intermediate regime of relatively short star chains, while the BoB model fails in correctly describing the plateau modulus of these short chains. From our point of view, both disparities have the same origin and, in the case of the TMA, can be solved by removing the high-frequency mode contribution to the contour length fluctuation of the primitive path. An excellent agreement between data and theory is then obtained for all molecular weights of the arms, which indicates the capability of the TMA to provide a quantitative prediction of the rheology of monodisperse star-shaped polymers. A very good agreement is also obtained with the BoB model, despite the expected discrepancy observed with short star chains. This proves the fact that current tube-based models are successful in quantitative predictions of linear rheology of monodisperse star-shaped polymers.