Mathematical modelling for TM topology under uniform and hotspot traffic patterns

Interconnection networks are introduced when dealing with the connection of a significant number of processors in massively parallel systems. TM topology is one of the latest interconnection networks to solve the deadlock problem and achieve high performance in massively parallel systems. This topology is derived from a Torus topology with removing cyclic channel dependencies. In this paper, we derive a mathematical model for TM topology under uniform and hotspot traffic patterns to compute the average delay. The average delay is formulated from the sum of the average delay of network, the average waiting time of the source node and the average degree of virtual channels. The results obtained from the mathematical model exhibit a close agreement with those predicted by simulation. In addition, sufficient simulation results are presented to revisit the TM topology performance under various traffic patterns.