| Summary: | 博士 === 國立交通大學 === 應用數學系所 === 93 === This thesis is divided into two types of networks: computer networks and switching networks used in communication. In particular, we will study a class of computer networks called the triple-loop network, and a class of switching networks called Log2(N, m, p). We first introduce the former.
A multi-loop network, denoted by ML(N; s1, …, sl), can be represented by a digraph on N nodes, 0, 1, …, N − 1 and lN links of l types: i → i + s1, i → i + s2, …, i → i + sl, (mod N), i = 0,1, …, N −1. The integers s1, …, sl are called the steps of the multi-loop network. When l is specified, we can also call it an l-loop network. In particular, when l = 2, the multi-loop network is usually called the double-loop network and is denoted by DL(N; s1, s2). When l = 3, the multi-loop network is usually called the triple-loop network and is denoted by TL(N; s1, s2, s3).
Several triple-loop networks have been recently proposed and their efficiency studied. However, the number of cases for which one of these networks exist is sparse. In this thesis, we extend these networks to larger classes to enhance their realizability. We also give a heuristic method to optimize the network parameters to increase their efficiency.
In this thesis, we study the k-diameters of three specific triple-loop networks. In particular, we construct three node-disjoint shortest paths no longer than the diameter plus 2 for any pair of nodes.
Next we introduce the Log2(N, m, p) network.
Lea and Shyy [32] first proposed the Log2(N, m, p) network with N = 2n inputs (outputs), which consists of a vertical stacking of p copies of BY-1(n, m), 0 �T m �T n�{1, sandwiched between and connected to an input stage and an output stage, each with N 1 �e p (or p �e 1) crossbars. Later, Hwang [24] extended the Log2(N, m, p) network to Logd(N, m, p) network by replacing the 2 �e 2 crossbars with d �e d crossbars.
A network is wide-sense nonblocking (WSNB) if the connection of the current request is assured only when all connections are routed according to a given algorithm. Traffic can be classified as point-to-point, like 2-party phone calls, or broadcast, which is one to all. If there is a restriction on the maximum number of receivers per request, then broadcast is called multicast (one to many), or f-cast, if that number is specified to be f.
Tscha and Lee [44] proposed a fixed-size window algorithm for the multicast Log2(N, 0, p) network and expressed a desire to see its extension to the Log2(N, m, p) network. Later, Kabacinski and Danilewicz [29] generalized the fixed-size window to variable size to improve the results. In this thesis, we further extend the variable-size results from the Log2(N, 0, p) network to Log2(N, m, p).
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