An Analytical Model for Torus Networks in the Presence of Batch Message Arrivals with Hot-spot Destinations

Interconnection networks are hardware fabrics supporting communications between individual processors in multi-computers. The low-dimensional k-ary n-cubes (or torus) with adaptive wormhole switching have attracted significant research efforts to construct high-performance interconnection networks in contemporary multi-computers. The arrival process and destination dis- tribution of messages have great effects on network performance. With the aim of capturing the characteristics of the realistic traffic pattern and obtaining a deep understanding of the performance behaviour of interconnection networks, this paper presents an analytical model to investigate the message latency in adaptive-routed wormhole-switched torus networks where there exists hot-spot nodes and the message arrivals follow a batch arrival process. Each generated message has a given probability to be directed to the hot-spot node. The average degree of virtual channel multiplexing is computed by the GE/G/1/V queueing system with finite buffer capacity. We compare analytical results of message latency with those obtained through the simulation experiments in order to validate the accuracy of the derived model.