## Load balancing and density dependent jump markov processes

We provide a new approach for analyzing both static and dynamic randomized load balancing strategies. We demonstrate the approach by providing the first analysis of the following model: customers arrive as a Poisson stream of rate {lambda}n, {lambda} < 1, at a collection of n servers. Each customer chooses some constant d servers independently and uniformly at random from the n servers, and waits for service at the one with the fewest customers. Customers are served according to the first-in first-out (FIFO) protocol, and the service time for a customer is exponentially distributed with mean 1. We call this problemmore »