1. For use with an address stream derived from the operation of a computer with single level storage, an emulation machine for use in determining the average time for completing memory reference operations in a multi-level storage by emulating the operation of said multi-level storage and thereby obtaining data from which said time can be determined, said machine comprising multiple directories for receiving and storing addresses from said address stream, one of said directories provided for each level of said multi-level storage other than the main storage level, each of said directories of a size capable of holding all addresses which the corresponding level in said multi-level storage could contain, comparator means connected to each of said directories for comparing the existing address contents of said directories with successive addresses from said address stream, updating means connected to said directories for updating the existing addresses in said directories as new addresses are received from said address stream, and counting means connected to said comparator means to provide a record of hits (compares) and misses (no compares) for fetch and store memory reference from said address stream at each of said directories whereby data is obtained from which the average time for completing memory references in said multi-level storage can be computed.