  We consider random-access networks where nodes represent servers with a queue
and can be either active or inactive. A node deactivates at unit rate, while it
activates at a rate that depends on its queue length, provided none of its
neighbors is active. We consider arbitrary bipartite graphs in the limit as the
initial queue lengths become large and identify the transition time between the
two states where one half of the network is active and the other half is
inactive. The transition path is decomposed into a succession of transitions on
complete bipartite subgraphs. We formulate a randomized greedy algorithm that
takes the graph as input and gives as output the set of transition paths the
network is most likely to follow. Along each path we determine the mean
transition time and its law on the scale of its mean. Depending on the
activation rates, we identify three regimes of behavior.
