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As VLSI technology continues to improve, circuit area is gradually being replaced by pin restrictions as the limiting factor in design. Thus, it is reasonable to anticipate that on-chip memory will become increasingly inexpensive since it is a simple, regular structure than can easily take advantage of higher densities.In this paper we examine one way in which this trend can be exploited to improve the performance of multistage interconnection networks (MINs). In particular, we consider the performance benefits of placing significant memory in each MIN switch. This memory is used in two ways: to store (the unique copies of) data items and to maintain directories. The data storage function allows data to be placed nearer processors that reference it relatively frequently, at the cost of increased distance to other processors. The directory function allows data items to migrate in reaction to changes in program locality. We call our MIN architecture the Memory Hierarchy Network (MHN).In a preliminary investigation of the merits of this design [8] we examined the performance of MHNs under the simplifying assumption that an unlimited amount of memory was available in each switch. We found that despite the longer switch processing times of the MHN, system performance is improved over simpler, conventional schemes based on caching.In this paper we refine the earlier model to account for practical storage limitations. We study ways to reduce the amount of directory storage required by keeping only partial information regarding the current location of data items. The price paid for this reduction in memory requirement is more complicated (and in some circumstances slower) protocols. We obtain comparative performance estimates in an environment containing a single global memory module and a tree-structured MIN. Our results indicate that the MHN organization can have substantial performance benefits and so should be of increasing interest as the enabling technology becomes available.