Minimizing the externalities variance in a LCFS-PR $M/G/1$ queue under various constraints

TL;DR

This paper investigates how to minimize the variance of externalities in an LCFS-PR M/G/1 queue, considering various constraints, to improve system efficiency and fairness.

Contribution

It introduces a novel approach to minimize externalities variance in LCFS-PR queues under multiple constraints, addressing a gap in queue management strategies.

Findings

Externalities variance can be effectively minimized under certain constraints.

The proposed methods improve fairness in service systems.

Analytical results demonstrate the impact of constraints on externalities.

Abstract

Consider a LCFS-PR $M/G/1$ queue and assume that at time $t = 0$, there are $n+2$ customers $c_1,c_2,...,c_{n+1},c$ who arrived in that order such that $t = 0$ is the arrival time of $c$. Then, the externalities which are generated by $c$ is the total waiting time that would be saved by $c_1,c_2,...,c_{n+1}$ if $c$ reduced his service requirement to zero. Motivated by some applications, this work is about the minimization of the externalities variance under various constraints.