Transient error approximation in a L\'evy queue

TL;DR

This paper analyzes transient errors in a Le9vy queue to improve capacity allocation by incorporating transient effects into cost functions, resulting in significant cost reductions demonstrated through numerical experiments.

Contribution

It introduces a refined cost function for transient queues using Le9vy process fluctuation theory, leading to improved capacity allocation rules.

Findings

Transient analysis reveals significant cost savings when correcting for non-stationary effects.

The refined capacity rule outperforms traditional stationary-based methods.

Numerical experiments confirm the practical impact of the proposed correction.

Abstract

Motivated by a capacity allocation problem within a finite planning period, we conduct a transient analysis of a single-server queue with L\'evy input. From a cost minimization perspective, we investigate the error induced by using stationary congestion measures as opposed to time-dependent measures. Invoking recent results from fluctuation theory of L\'evy processes, we derive a refined cost function, that accounts for transient effects. This leads to a corrected capacity allocation rule for the transient single-server queue. Extensive numerical experiments indicate that the cost reductions achieved by this correction can by significant.