The application of metamodeling to interconnection network analysis

Metamodeling is demonstrated as a methodology to accurately and concisely characterize the behavior of parallel processing interconnection networks. A set of mathematical metamodels are derived from a discrete event simulation model and then used to predict and compare the performance of interconnection networks. To illustrate the development and the application of metamodels, models for the multistage cube network, the single stage cube network (hypercube), and the Iliac IV mesh-type network are formulated. These models, validated using empirical data from earlier studies, provide compact mathematical relations between packet delay time, message load, and switch size for each interconnection architecture. This approach provides insight into the complexities of network performance and uses simulation as the experimental vehicle for theoretical development. We show the comparison of network performance and conclude that the use of simulation as a means to estimate mathematical models is beneficial and consistent with experimental evidence. Our metamodels for performance prediction establish a basis for future comparisons that can be directly applied by other researchers. The models give the designer of a parallel processing system additional insight for choosing the interconnection network which best suits the application needs.