  In the present paper, we study the evolution of an overloaded cyclic polling
model that starts empty. Exploiting a connection with multitype branching
processes, we derive fluid asymptotics for the joint queue length process.
Under passage to the fluid dynamics, the server switches between the queues
infinitely many times in any finite time interval causing frequent oscillatory
behavior of the fluid limit in the neighborhood of zero. Moreover, the fluid
limit is random. Additionally, we suggest a method that establishes finiteness
of moments of the busy period in an M/G/1 queue.
