In: International Journal on Modeling and Simulation, Vol. 19, No. 4, pages 189-196. 1999.
Abstract: Many multi-stage interconnection networks (MINs) and single stage interconnection networks (SINs) have been proposed for parallel computer systems and for fast packet switching in high-speed networks. The cost, performance and fault-tolerance capability of the interconnection networks (INs) becomes very important in the design considerations of a multiprocessor system. Several types of INs have been proposed, notably multi-stage and singe stage INs. There have been extensive studies in MINs but relatively little work on SINs has appeared in the literature. This paper reevaluates he unbuffered Beta topology of SIN using stochastic Petri nets. An approximate analytical model is also presented. The random delay experienced by a message traversing the network with a uniform traffic is analyzed. Messages can have different sizes. Each sender can accept one packet per cycle and route it to approximate receiver. It is shown that the bandwidth increase when the data transfer increases. In addition, it is shown that the average transfer time increases slowly compared to the increase of the number of processors. The advantages of the proposed model include modeling with acceptable numbers of states and easy generalizations of the model.
Keywords: interconnecting networks, performance modeling, stochastic Petri nets.