MVAMIN: Mean value analysis algorithms for multistage interconnection networks

Abstract

A new approach to the modeling of multistage interconnection networks (MIN) based on queueing theory is presented in this paper. The network operates in an asynchronous, decentralized packet-switched mode and has buffers at each queueing center. The analytical approach involves basically three steps, namely, the building of a closed multiclass queueing model for the MIN system, the derivation of input parameters for the model, and finally solving the model using a heuristic mean value analysis algorithm. Networks operating in both tightly coupled and loosely coupled environments are analyzed. Separate networks are assumed for packets from processors to memories and from memories to processors in the case of a tightly coupled system. We derive a set of routing equations corresponding to the probabilities of memory requests through which systems with arbitrary memory reference patterns can be analyzed. Here, N is the number of processors or memories with n = log 2 N number of stages. An approximate technique of aggregation is also developed to significantly reduce the computational complexity of the above analysis while maintaining the accuracy of the model. The accuracy of our models has been verified by comparing the analytical results with those obtained from simulation. The simulations are based on 95% confidence level with a relative confidence interval width of 0.005.