Research On Communication Delay Of Exponential-step Loop Networks

Topology is widely used in production management,military scheduling,transportation,and high performance computing.The topology consists of nodes and wires.The most important metrics are communication latency and average communication latency.In the field of high performance computing,high performance computer systems expect the lowest possible communication latency and construction cost.That is,when the topology is simple and the number of switches and physical links is as small as possible,the communication delay and the average communication delay are as small as possible.Increasing node size can reduce communication latency in the topology,but the increase in switches and physical links greatly increases the cost of network construction and operation.Therefore,the design of appropriate step scheme has become an important means to improve the communication delay of topology.Fixed-step is traditionally adopted for design,but the diameter of fixed-step ring network is no longer smaller than the lower bound given by Coppersmith and Wong.In recent years,it has been proposed to construct a topology with random-step,and the communication delay of the resulting topology is far less than the lower bound of the topology with fixed-step.In this paper,the exponential step is used to construct the topology,and the algorithm for generating the exponential step directed,undirected multi-ring network topology is designed.Then,according to the adjacency matrix and Floyd algorithm,the diameter and average diameter of the exponential-step ring network topology are given.According to the above algorithm,a simulation platform is developed with Visual Studio C#.After the topology parameters are input,the corresponding ring network topology can be generated,and its diameter and average diameter and other performance parameters can be calculated.In order to fully study the characteristics of exponential-step topology,a series of distributions of exponential-step ring network topology were generated through simulation by changing the number of nodes N and node degree K,and a series of diameters and average diameters were obtained,and compared with the diameters and average diameters of traditional fixed and random step ring network.The results show that the diameter and average diameter of the exponential-step ring network are smaller than those of the traditional fixed-step network and random-step ring network.