Uniqueness of a constrained variational problem and large deviations of buffer size

TL;DR

This paper proves the global uniqueness of solutions to certain constrained variational problems and applies these results to analyze large deviations in buffer overflow probabilities in multi-dimensional models.

Contribution

It introduces a novel approach to establish the essential uniqueness of solutions in large deviations problems related to buffer models.

Findings

Proves global uniqueness of solutions to constrained variational problems.

Establishes the essential uniqueness of solutions in multi-dimensional large deviations.

Analyzes the probability and typical paths to buffer overflow in small buffer limits.

Abstract

We show global uniqueness of the solution to a class of constrained variational problems, using scaling properties. This is used to establish the essential uniqueness of solutions of a large deviations problem in multiple dimensions. The result is motivated by models of buffers, and in particular the probability of, and typical path to overflow in the limit of small buffers, which we analyze.