發展一般化蜂巢環圈網路以應用在智慧型隧道偵測控制資料擷取(SCADA)網路之設計為例

Abstract

一般環形網路(度數(degree)為二)往往考量有一條"節線"容錯(fault tolerance)的特性與提供可有序地查核維修的機制，但對於網路上"節點"之破壞防患通常最多僅考量備份(spare)的觀點，但備份的節點在平時並未構成整體營運的一部份，一旦事變其啟動時差等因素會影響即時應變的能力；本論文提出節點成對、度數為三的蜂巢矩形環圈(HReT, honeycomb rectangular torus)與一般化蜂巢環圈(GHT, generalized honeycomb torus)網路模式供隧道內偵測控制資料擷取(SCADA)網路之應用。本論文數學証明蜂巢矩形環圈網路的特性：證明蜂巢矩形環圈上任一節線斷落，網路上各節點可維持漢彌頓特性；在縱向節點數目至少為六或橫向節點數目僅為二但縱向節點數目至少為四的狀況，證明蜂巢矩形環圈上任一對異性之(biparpite)節點損壞，網路上其他各節點仍可維持漢彌頓特性。本論文數學証明一般化蜂巢環圈網路的特性：証明蜂巢矩形環圈、蜂巢環圈(HT, honeycomb torus)可以同構成一般化蜂巢環圈網路；蜂巢環圈可屬一種管形之一般化蜂巢環圈網路；並證明管形之一般化蜂巢環圈網路可保有環狀之漢彌頓特性，有利於在單管形空間配置同時具有節線與節點容錯性暨提供可有序地查核維修的機制。

The ring network of regular degree-2 nodes is generally utilized for links' fault tolerance as well as providing a mechanism supporting orderly inspection and maintenance, and spare may be arranged to support nodes' fault tolerance. However, spares are inefficiently used in normal conditions and may have difficulties to support real-time processing. Therefore, in this dissertation, HReT (honeycomb rectangular torus) and GHT (generalized honeycomb torus) networks of degree-3 dual-nodes are studied for promoting the capability of the SCADA (Supervisory Control And Data Acquisition) network in tunnels. The following HReT network features are mathematically proved: HReT (m,n) is 1-edge hamiltonian, and HReT(m,n) is 1_p-hamiltonian if and only if either n ³ 6 or m = 2 and n ³ 4, HReT(m,n)-F can keep hamiltonian when F={a,b} with a in A and b in B, A and B are bipartite nodes’ groups. The following GHT network features are mathematically proved: HReT network and HT (honeycomb torus) can be isomorphic to GHT network, and HT can be a specific single-tube shaped GHT which can keep hamiltonian when one edge is broken and have both links’ and nodes’ fault tolerance as well as a mechanism supporting orderly inspection and maintenance.