We consider the problem of designing a network of optical cross-connects (OXCs) to provide end-to-end lightpath services to large numbers of label switched routers (LSRs). We present a set of heuristic algorithms to address the combined problem of physical topology design (i.e., determine the number of OXCs required and the fiber links among them) and logical topology design (i.e., determine the routing and wavelength assignment for the lightpaths among the LSRs). Unlike previous studies which were limited to small topologies with a handful of nodes and a few tens of lightpaths, we have applied our algorithms to networks with hundreds or thousands of LSRs and with a number of lightpaths that is an order of magnitude larger than the number of LSRs. In order to characterize the performance of our algorithms, we have developed lower bounds which can be computed efficiently. We present numerical results for up to 1000 LSRs and for a wide range of system parameters such as the number of wavelengths per fiber, the number of transceivers per LSR, and the number of ports per OXC. The results indicate that it is possible to build large-scale optical networks with rich connectivity in a cost-effective manner, using relatively few but properly dimensioned OXCs. 相似文献
Various fit indices exist in structural equation models. Most of these indices are related to the noncentrality parameter (NCP) of the chi-square distribution that the involved test statistic is implicitly assumed to follow. Existing literature suggests that few statistics can be well approximated by chi-square distributions. The meaning of the NCP is not clear when the behavior of the statistic cannot be described by a chi-square distribution. In this paper we define a new measure of model misfit (MMM) as the difference between the expected values of a statistic under the alternative and null hypotheses. This definition does not need to assume that the population covariance matrix is in the vicinity of the proposed model, nor does it need for the test statistic to follow any distribution of a known form. The MMM does not necessarily equal the discrepancy between the model and the population covariance matrix as has been assumed in existing literature. Bootstrap approaches to estimating the MMM and a related quantity are developed. An algorithm for obtaining bootstrap confidence intervals of the MMM is constructed. Examples with practical data sets contrast several measures of model misfit. The quantile-quantile plot is used to illustrate the unrealistic nature of chi-square distribution assumptions under either the null or an alternative hypothesis in practice.