Lowest priority waiting time distribution in an accumulating priority L\'evy queue

TL;DR

This paper introduces a novel approach to derive the waiting time distribution for the lowest priority class in an accumulating priority queue with Le9vy input, using workload overtaking and first-passage time analysis.

Contribution

It presents a new method based on workload overtaking and stopping times to analyze waiting times in Le9vy-driven AP queues, which was not previously available.

Findings

Derived the waiting time distribution for the lowest class in an AP Le9vy queue.

Established a workload overtaking process framework.

Solved a first-passage time problem for queue analysis.

Abstract

This paper presents a new method for deriving the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive L\'evy input. The priority of a non-atomic customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. The method relies on the construction of a workload overtaking process and solving a first-passage time problem using an appropriate stopping time.