Optimization of the fluid model of scheduling: local predictions

TL;DR

This paper develops a continuous fluid model for resource scheduling in queuing systems, providing local predictions and an explicit algorithm for minimizing queue delays under certain conditions.

Contribution

It introduces a local prediction method and an explicit convex optimization algorithm for queue delay minimization in fluid models.

Findings

Algorithm delivers explicit solutions for delay minimization.

Applicable to convex optimization on polytopes.

Addresses uniform steadiness in queuing systems.

Abstract

In this research a continuous model for resource allocations in a queuing system is considered and a local prediction on the system behavior is developed. As a result we obtain a set of possible cases, some of which lead to quite clear optimization problems. Currently, the main result of this research direction is an algorithm delivering an explicit solution to the problem of minimization of the sum of all queues mean delays (which is not the overall mean delay) in the case of the so-called uniform steadiness. Basically, in this case we deal with convex optimization on a polytope.