The competitive ratio is the most common metric in online algorithm analysis. Unfortunately, it produces pessimistic measures and often fails to distinguish between paging algorithms that have vastly differing performance in practice. An apparent reason for this is that the model does not take into account the locality of reference evidenced by actual input sequences. Therefore many alternative measures have been proposed to overcome the observed shortcomings of competitive analysis in the context of paging algorithms. While a definitive answer to all the concerns has yet to be found, clear progress has been made in identifying specific flaws and possible fixes for them. In this paper we consider two previously proposed models of locality of reference and observe that even if we restrict the input to sequences with high locality of reference in them the performance of every on-line algorithm in terms of the competitive ratio does not improve. Then we prove that locality of reference is useful under some other cost models, which suggests that a new model combining aspects of both proposed models can be preferable. We also propose a new model for locality of reference and prove that the randomized marking algorithm has better fault rate on sequences with high locality of reference. Finally we generalize the existing models to several variants of the caching problem.