One aspect of network design is the extent to which memory is shared among the processing elements. In this paper a model with limited sharing (only two processors connected to each memory) is analyzed and its performance compared with the performance of two other models that have appeared in the literature. One of these is a model of multiple processors sharing a single memory; the other model considers a multiprocessor configuration in which each processor has its own dedicated memory. The tasks processed by these networks are described by both time and memory requirements. The largest-memory-first (LMF) scheduling algorithm is employed and its performance with respect to an enumerative optimal scheduling algorithm is bounded. On the basis of this measure we conclude that memory sharing is only desirable on very small networks and is disadvantageous on networks of larger size.