Working memory is a core concept in cognition, predicting about 50% of the variance in IQ and reasoning tasks. A popular test of working memory is the complex span task, in which encoding of memoranda alternates with processing of distractors. A recent model of complex span performance, the Time-Based-Resource-Sharing (TBRS) model of Barrouillet and colleagues, has seemingly accounted for several crucial findings, in particular the intricate trade-off between deterioration and restoration of memory in the complex span task. According to the TBRS, memory traces decay during processing of the distractors, and they are restored by attentional refreshing during brief pauses in between processing steps. However, to date, the theory has been formulated only at a verbal level, which renders it difficult to test and to be certain of its intuited predictions. We present a computational instantiation of the TBRS and show that it can handle most of the findings on which the verbal model was based. We also show that there are potential challenges to the model that await future resolution. This instantiated model, TBRS*, is the first comprehensive computational model of performance in the complex span paradigm. The Matlab model code is available as a supplementary material of this article.