  Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed,
network modeling has been studied intensively in light of the network growth
and the preferential attachment (PA). However, numerous real systems are
featured with a dynamic evolution including network reduction in addition to
network growth. In this paper, we propose a novel mechanism for evolving
networks from the perspective of vertex degree. We construct a queueing system
to describe the increase and decrease of vertex degree, which drives the
network evolution. In our mechanism, the degree increase rate is regarded as a
function positively correlated to the degree of a vertex, ensuring the
preferential attachment in a new way. Degree distributions are investigated
under two expressions of the degree increase rate, one of which manifests a
``long tail'', and another one varies with different values of parameters. In
simulations, we compare our theoretical distributions with simulation results
and also apply them to real networks, which presents the validity and
applicability of our model.
