Maximally Stabilizing Task Release Control Policy for a Dynamical Queue

TL;DR

This paper models a dynamical queue influenced by human performance laws, proposing a threshold-based task release policy that maximizes stability at the highest possible deterministic arrival rate.

Contribution

It introduces a new queueing model based on empirical human performance laws and designs an optimal threshold policy for maximum queue stability.

Findings

Established an upper bound on stabilizable arrival rate.

Proposed a simple threshold policy for task release.

Proved the policy achieves maximum stability.

Abstract

In this paper, we introduce a model of dynamical queue, in which the service time depends on the server utilization history. The proposed queueing model is motivated by widely accepted empirical laws describing human performance as a function of mental arousal. The objective of this paper is to design task release control policies that can stabilize the queue for the maximum possible arrival rate, assuming deterministic arrivals. First, we prove an upper bound on the maximum possible stabilizable arrival rate for any task release control policy. Then, we propose a simple threshold policy that releases a task to the server only if its state is below a certain fixed value. Finally, we prove that this task release control policy ensures stability of the queue for the maximum possible arrival rate.