The hydrodynamic limit of a randomized load balancing network [article]

Reza Aghajani, Kavita Ramanan
2017 arXiv   pre-print
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
more » ... vice 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.
arXiv:1707.02005v2 fatcat:fj2jzpzkmfaobinfeitwlfnaay