Out of equilibrium functional central limit theorems for a large network where customers join the shortest of several queues

2 00 3 Out of equilibrium functional central limit theorems for a large network where customers join

Customers arrive at rate N α on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate β. We let N go to infinity. We prove a functional central limit theorem (CLT) for the tails of the empirical measures of the queue occupations, in a Hilbert space with the weak topology, with limit given by an Ornstein-Uhlenb...

Functional Central Limit Theorems for a Large Network in Which Customers Join the Shortest of Several Queues Functional Central Limit Theorems for a Large Network in Which Customers Join the Shortest of Several Queues

We considerN single server infinite buffer queues with service rate β. Customers arrive at rateNα, choose L queues uniformly, and join the shortest. We study the processes t ∈ R+ 7→ R t = (R t (k))k∈N for large N , where R t (k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We cons...

A functional central limit theorem in equilibrium for a large network in which customers join the shortest of several queues

2 00 3 A functional central limit theorem in equilibrium for a large network in which customers join the shortest of several queues

We consider N single server infinite buffer queues with service rate β. Customers arrive at rate N α, choose L queues uniformly, and join the shortest one. The stability condition is α < β. We study in equilibrium the fraction of queues of length at least k ≥ 0. We prove a functional central limit theorem on an infinite-dimensional Hilbert space with its weak topology, with limit a stationary O...

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

We considerN single server infinite buffer queues with service rate β. Customers arrive at rate Nα, choose L queues uniformly, and join the shortest. We study the processes t ∈ R+ 7→ R t = (R t (k))k∈N for large N , where R t (k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We con...