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

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.