A Foreground-Background queueing model with speed or capacity modulation

TL;DR

This paper develops a queueing model with dynamic speed or capacity control, analyzing trade-offs between costs and energy, and provides exact solutions with numerical insights into system behavior.

Contribution

It introduces a novel queueing model with Coxian service times and dynamic control, offering exact solutions and exploring cost trade-offs in system management.

Findings

Exact solutions for two-dimensional Markov processes

Counter-intuitive results on cost trade-offs

Numerical experiments illustrating system dynamics

Abstract

The models studied in the steady state involve two queues which are served either by a single server whose speed depends on the number of jobs present, or by several parallel servers whose number may be controlled dynamically. Job service times have a two-phase Coxian distribution and the second phase is given lower priority than the first. The trade-offs between holding costs and energy consumption costs are examined by means of a suitable cost functions. Two different two-dimensional Markov process are solved exactly. The solutions are used in several numerical experiments. Some counter-intuitive results are observed.