In this paper we analyze measurements gathered from a 2.5 Gbps link in the Finnish university network (Funet) in 2004. The traffic is broken down into origin-destination (OD) pair components based on source and destination IP address. We study the traffic characteristics of these components, and identify four typical representative OD pairs. For these pairs we investigate the validity of a moving IID Gaussian model. We find that the statistical properties of these OD pairs differ significantly from each other, with only some of them close to Gaussian. The OD pairs are also found to have some cross-correlation between each other, contradicting an often made assumption about OD pair independence. Furthermore, the existence of a mean-variance relation between the OD pairs is studied. We find that there is a relation between mean and variance, but for some periods of time it is rather weak.