Functional central limit theorems for a large network in which customers join the shortest of several queues

@inproceedings{Graham2004FunctionalCL,
  title={Functional central limit theorems for a large network in which customers join the shortest of several queues},
  author={Carl Graham},
  year={2004}
}
We consider N single server infinite buffer queues with service rate β. Customers arrive at rate Nα, chooseL queues uniformly, and join the shortest. We study the proces sest ∈ R+ 7→ R t = (R t (k))k∈N for largeN , whereR t (k) is the fraction of queues of length at least k at timet. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] an d Graham [5]. We consider certain Hilbert spaces with the weak topology. First, we prove a functional c entral limit theorem… CONTINUE READING