Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Lakhmi C. Jain; N.M. Martin
CRC Press, CRC Press LLC
ISBN: 0849398045   Pub Date: 11/01/98
  

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4.2 Assumptions and Constraints

In order to obtain an acceptable network topology, let us call it a regular topology, different requirements, limitations, and routing rules have to be fulfilled.

The network topology must fulfill the following requirements: all node-to-node connections should be established through the two shortest, mutually independent paths, primary and spare, the same for both directions of communication, ensuring network survivability in the case of single network element failure, the link or node.

A link failure is assumed to be caused by a failure in an optical amplifier, or in the fiber cable, causing an interruption of all services in the cable.

The following definition is assumed: a node-to-node connection is available if both directions of the connection are available.

The traffic requirements between all pairs of nodes are given. All link capacities are multiples of 2.5 Gbit/s (standard capacity in digital transmission), achieved through a number of wavelengths in one or more different optical fibers on the same optical link. The node pair direct distances are derived from the road distances between major European cities. Because of the accumulated noise and distortions in optical fibers, amplifiers, and node elements, the optical path length limitation is fixed at 2000 km. The distances between optical amplifiers are assumed to be maximum 100 km. Component failure and repair rate data for calculating the unavailability of the future all-optical network are taken from the existing data set for mature optical components, whereas, for new photonic components, the calculation is based on estimated data. Steady-state unavailability (the asymptotic value of unavailability if time tends to infinity) is considered, assuming constant failure and repair rates. In the total path unavailability calculation, the impact of node unavailabilities is negligible compared to the unavailabilities of optical links.

4.3 Cost Evaluation

The cost model applied in the network availability optimization was taken from [13]. The total network cost for the set of nodes N is a sum of all link and node costs is

where CLij is the cost of the link between nodes i and j, and CNi is the cost of the node i. Link cost is a function of link length Lij (km) and link capacity Vij (Gbit/s),

The link capacity is determined for each link by summing up the contributions from all primary and spare paths that make use of it.

The node cost CNi is a function of node effective distance Ni (km) (Ni represents the cost of node in equivalent distance terms), and the total capacity of all links incident to the node — Vi (Gbit/s):

where di is node degree (the number of links incident to node i), E and F constants assumed to be 200 km and 100 km, respectively.

4.4 Shortest Path Evaluation

For each topology, the solution proposed by GA between all pairs of nodes — the first shortest path as the primary path, and the second shortest path as a spare path — have to be evaluated using Dijkstra algorithm. The weights Wij of links to be used in shortest path evaluation reflect the influence of node parameters on the path “length”.

4.5 Capacity Evaluation

Superposing all traffic requirements between all pairs of nodes, using primary and spare paths, the capacities of links and nodes are obtained.

4.6 Network Unavailability Calculation

Network unavailability is defined as the worst case of all node-to-node connection unavailabilities (source-termination unavailability) [14]:

where Uk is the unavailability of a link from the primary path (pp), and Ul, is the unavailability of a link from the independent spare path (sp). In other words, the unavailability model of a node-to-node connection could be described as a serial structure of two parallel.

Optical link is treated as a nonredundant structure comprising fiber in optical fiber cable and optical amplifiers. For small unavailability values of link elements, an approximate formula for the total link unavailability can be used.

where λF is fiber cable failure rate per km, λOA is the failure rate of the optical amplifier (OA), NOA is the number of optical amplifiers on the link, L is the link length, MTTRF and MTTROA are mean times to repair of fiber (F) and OA, respectively (λF = 114 fit/km, MTTRF = 21 hours, λOA = 4500 fit, MTTROA = 21 hours, fit = number of failures per 109 hours).

4.7 Solution Coding

Possible solutions are coded as binary strings with n(n-1)/2 bits. The position of every bit represents one direct link between two nodes. The value of the bit corresponding to 1 represents the existence of the link in the solution, while the value 0 stands for a missing corresponding link.

For instance, the case study network of 11 nodes should be coded by the string containing 55 bits. In the Figure 14 one random string is presented and corresponding network is shown in the Figure 15.


Figure 14  An example of coded topology in the case study.


Figure 15  The topology representing a random string shown in Figure 14.


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