Study On Some Fundamental Problems Of Optical Communication Networks

Wavelengths are limited resource in WDM networks. State-of-the-art technology allows close to 300 wavelengths in the laboratory. However, less than 64 wavelengths can be used in real systems. Thus how to make wavelength assignment is crucial for taking full advantage of the potential of WDM networks. The load of a network is a lower bound of the wavelength needed under the condition of fulfilling the communication request, this parameter measures the situation of wavelengths assignment, and it is also one of the most important factors in routing stratge. So it is one of the most significant and extensively studied problems in communication networks. Wavelength assignment is another fundamental problem which aims at how to assign the wavelength to the connections between the nodes pair efficiently, this problem is usually resolved by coloring of edges or vertices of graph. Reliability is an important index of a network's performance, fault-tolerant is basic measure to enhance the reliability, thus it is also a fundamental problems studied in WDM networks.Multi-hop and Single-hop are the basic communication mode of optical networks; the problems mentioned above are studied in this dissertation under these two conditions. The method used to resolve problems are mainly graph theory and combinatorics.The main achievements in this dissertation are listed as follow.(1) In single-hop system and all-to-all communication mode, We proposed a type of directed double-loop networks with fault tolerant routing R₁(D) which is composed of shortest path and the path equal or just longer than the shortest path, according to the given routing R₁(D) the load of each arc is equal and minimal among the same size of directed double-loop networks. We proved that the *****(R₁(D)) ofD(n;1,h),11(D))=h³-4h+3,if n=h²-l;h=2, 3,4,……, furthermore this kinds of double-loop network have better reliabilitybecause it is 1 fault-tolerant. Under the all-to-all communication mode and shortest path routing , we got another result which shows that the load of an edge in a Kautz network K(d, k) is upper bounded by 1+2d+3d²+…+kd^k-1.The sufficient-necessary condition for the load of an edge to reach this bound is also given. This result implies that if d≤2+(?),then the load of the Kautz network l(K(d, k))=1+2d+3d²+*****+kd^k-1. This means in order to get lower network load we need to find other routing strategy other than the shortest path routing.(2) Proposed a solution to wavelength problem of Cartesian network with multi-hops. An upper bound of the (uniform) wavelength index is established. This result leads to a consequence for the n-th power of arbitrary network with k-hops. As an application, we point out that a tight upper bound for Hamming graph with k-hops is p(?). The solution is valuable to further research and applicationbecause of its practicability.(3) A fault tolerant routing strategy for all optical Johnson networks J(n, k) is proposed, according to this routing strategy the source nodes and destination nodes pair of Johnson network are connected by k paths , these paths are either equal to shortest path or the path just 1 step longer than the shortest path.The results and the method resolving problems in this dissertation will expand the study of similar problems and lay a ground for further research on these problems. In particular, the method of routing and wavelength assignment in Cartesian network can be applied in real optical networks.