This paper investigates the online k-taxi problem with a new feature that partial information about future service requests is provided in advance when deciding which taxi should be dispatched to serve the current request, whereas none of this is known in the traditional online k-taxi problem. Benefited by the foreknowledge, improved covering strategies are proposed for the problem in different scenarios with respect to the information known in advance. Following that, the value of foreknowledge in the online k-taxi problem with this new feature is quantified in the form of improved competitive ratios. It is proved that in some special cases, the competitive ratios are decreased from 1 + λ to (3 + λ)/2, where λ is a parameter determined by the metric space in which the problem is discussed. Furthermore, it is also shown that, in all cases, the improved covering strategies would never perform wore than the classical position maintaining strategy. In addition to these theoretical analyses, some numerical examples are presented to illustrate the proposed online strategies and their performances in practice as well.