3.3 Modelling Networks with Limited Wave- Length Conversion 6. References 3.2 Modelling Wdm Networks with Xed Alternate Routing

analysis requires the separate enumeration of the occupancy for every wavelength on every link used by multiple alternate routes for a single source-destination pair. In a network with F wavelengths per link, and with m links used by multiple alternate routes for a given source-destination pair, the calculation time required is exponential with the product of the number of wavelengths and number of multiple links (F:m). Thus, the computational requirements rapidly become excessive, limiting the application of this analysis to networks with few common links between alternate routes for a common source-destination pair, and to networks with few wavelengths on these links. The advantage of this analytical model of WDM networks compared with existing analyses is the wide range of WDM networks to which the technique can be applied. Unlike previous analytical models for WDM networks, this technique allows the analysis of networks which have logical paths between a source and destination which share common links and wavelengths, without assuming their independence. This was discussed in Section 3.2 for networks with xed alternate routing. By redeening the set of logical paths through the wavelengths and links within the network, networks with various forms of limited wavelength conversion 2,8,10] can also be modelled. However, the computational requirements of this model are often excessive when it is applied to networks with limited wavelength conversion due to the exponential nature of the complexity of the calculation. 4. CONCLUSION In this paper, we have presented an analytical model for analysing the performance of WDM networks with lowest-index wavelength assignment and xed alternate routing. This model can be applied to wavelength-continuous WDM networks with xed alternate routing, or to networks with limited wavelength conversion. Analytical models using both one-moment and two-moment descriptions of the overrow traac from wavelengths and routes were considered. The accuracy of each model was examined and shown to be adequate in a variety of networks. Erlang loss formula One stream; calculated Two streams; calculated Four streams; calculated Figure 6: Blocking probability versus ooered load for a one-hop route with multiple traac streams. ability decreases. Thus, when large numbers of streams are aggregated onto a link, the blocking probability is underestimated. The analytical model developed can be used to analyse wavelength-continuous networks with xed alternate routing and lowest-index wavelength assignment. In this section, we implement route and wavelength assignment by choosing to allocate a new connection to the rst available wavelength and …