Research On Triple-tight Optimality Of Double-loop Network And Simulation Of Network With Random-step

For those situations requiring ultra high speed communication networks,for example,as the communication network between CPU clusters of supercomputers,information communication delay is undoubtedly the most important.The computing speed of a single CPU of supercomputer is extremely fast,but if the information communication delay between them is larger,the overall computing speed would be greatly reduced.Thus,it is very important to study the low information communication delay network.Directed double loop network is just a communication network used in these situations.The thesis studies the information communication delay of the directed double loop network in every respect,the concept of "diameter variance" and "triple-tight optimality" are proposed,through the mathematical theoretical derivation and the programming simulation,it is proved that the "triple-tight optimal" directed double loop network is the network with the least information communication delay,and a cluster of directed double loop networks with "triple-tight optimality" is found in the simulation example.The thesis also studies the "triple-tight optimality" of the directed double loop network with random step,it is verified that the directed double loop network with random step is better than the ones with fixed step by programming simulation,and a cluster of "triple-tight optimal" directed double loop networks with random step is found in the simulation example.The main work of The thesis is as follows:1.On mathematical theoretical derivation,“step search method” is proposed,the properties of the “vertex relation tree” are proved,the upper and lower bounds of the diameter of directed double loop networks are derived,an explicit formula for calculating the mean diameter of directed double loop networks is derived,the upper and lower bounds of mean diameter are derived.The "buckets effect" in network communication is found,the definition formula of diameter variance is proposed,an explicit formula and an approximate estimation formula of diameter variance are derived.An approximate estimation formula of the sample variance of a linear varying statistical array is derived.The upper and lower bounds of the diameter variance are derived.The definition of "triple-tight optimality" of directed double loop networks is proposed.2.On programming simulation,algorithms for calculating the diameter,mean diameter and diameter variance of directed double loop networks are proposed,and these algorithms are simulated,the "triple-tight optimal" directed double loop networks are found in the simulation examples.A new algorithm for generating directed doubleloop networks with random step is proposed,and the algorithm is simulated.Algorithms for calculating the diameter,mean diameter and diameter variance of directed double loop networks with random step are proposed,pseudo code is given and these algorithms are simulated,the "triple-tight optimal" directed double loop networks with random step are found in the simulation examples.