Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-field Dynamics of Load-Balancing Networks with General Service
  Distributions   We introduce a general framework for the mean-field analysis of large-scale
load-balancing networks with general service distributions. Specifically, we
consider a parallel server network that consists of N queues and operates under
the $SQ(d)$ load balancing policy, wherein jobs have independent and identical
service requirements and each incoming job is routed on arrival to the shortest
of $d$ queues that are sampled uniformly at random from $N$ queues. We
introduce a novel state representation and, for a large class of arrival
processes, including renewal and time-inhomogeneous Poisson arrivals, and mild
assumptions on the service distribution, show that the mean-field limit, as $N
\rightarrow \infty$, of the state can be characterized as the unique solution
of a sequence of coupled partial integro-differential equations, which we refer
to as the hydrodynamic PDE. We use a numerical scheme to solve the PDE to
obtain approximations to the dynamics of large networks and demonstrate the
efficacy of these approximations using Monte Carlo simulations. We also
illustrate how the PDE can be used to gain insight into network performance.

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci