  Randomized load balancing networks arise in a variety of applications, and
allow for efficient sharing of resources, while being relatively easy to
implement. We consider a network of parallel queues in which incoming jobs with
independent and identically distributed service times are assigned to the
shortest queue among a randomly chosen subset of $d$ queues, and leave the
network on completion of service. Prior work on dynamical properties of this
model has focused on the case of exponential service distributions. In this
work, we analyze the more realistic case of general service distributions. We
first introduce a novel particle representation of the state of the network,
and characterize the state dynamics via a sequence of interacting
measure-valued stochastic processes. Under mild assumptions, we show that the
sequence of scaled state processes converges, as the number of servers goes to
infinity, to a hydrodynamic limit that is characterized as the unique solution
to a countable system of coupled deterministic measure-valued equations. We
also establish a propagation of chaos result that shows that finite collections
of queues are asymptotically independent. The general framework developed here
is potentially useful for analyzing a larger class of models arising in diverse
fields including biology and materials science.
