We study the performance of a family of cache replacement algorithms. The cache is decomposed into lists. Some of these lists can be virtual in the sense that only meta-data is stored in those lists. An item enters the cache via the first list and jumps to the next list whenever a hit on it occurs. The classical policies FIFO, RANDOM, CLIMB and its hybrids are obtained as special cases. We present explicit expressions for the cache content distribution and miss probability under the IRM model. We develop an algorithm with a time complexity that is polynomial in the cache size and linear in the number of items to compute the exact miss probability. We introduce lower and upper bounds on the latter that can be computed in a time that is linear in the cache size times the number of items. We introduce a mean field model to approximate the transient behavior of the miss probability and prove that this model becomes exact as the cache size and number of items go to infinity. We show that the set of ODEs associated to the mean field model has a unique fixed point that can be used to approximate the miss probability in case the exact computation is too time consuming. Using this approximation, we provide guidelines on how to select a replacement algorithm within the family considered such that a good trade-off is achieved between the cache reactivity and its steady-state hit probability. We simulate these cache replacement algorithms on traces of real data and This paper is an extended version of a conference paper [29]. The key addition of this journal version is the introduction of the notion of virtual lists in which only meta-data is stored. show that they can outperform LRU. Finally, we also disprove the well-known conjecture that the CLIMB algorithm is the optimal finite-memory replacement algorithm under the IRM model.