Queueing systems with renovation vs. queues with RED. Supplementary Material

TL;DR

This paper analytically compares M/D/1/N queues with renovation to queues with RED, focusing on performance metrics like loss rate and system moments, to evaluate their relative effectiveness.

Contribution

It provides explicit analytical expressions for key performance measures of M/D/1/N queues with renovation, facilitating comparison with RED mechanisms.

Findings

Derived formulas for stationary loss rate.

Calculated moments of the number in the system.

Facilitated comparison between renovation and RED queues.

Abstract

In this note we consider M/D/1/N queue with renovation and derive analytic expressions for the following performance characteristics: stationary loss rate, moments of the number in the system. Moments of consecutive losses, waiting/sojourn time are out of scope. The motivation for studying these characteristics is in the comparison of renovation with known active queue mechanisms like RED.