We study the biased random walk process in random uncorrelated networks with
arbitrary degree distributions. In our model, the bias is defined by the
preferential transition probability, which, in recent years, has been commonly
used to study efficiency of different routing protocols in communication
networks. We derive exact expressions for the stationary occupation
probability, and for the mean transit time between two nodes. The effect of the
cyclic search on transit times is also explored. Results presented in this
paper give the basis for theoretical treatment of the transport-related
problems on complex networks, including quantitative estimation of the critical
value of the packet generation rate.Comment: 5 pages (Phys. Rev style), 3 Figure