We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal 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. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.
Bibliographical noteFunding Information:
We wish to thank an anonymous referee whose helpful comments helped improve this paper. This work was supported in part by grant 1462/13 from the Israel Science Foundation and the Vigevani Chair in Statistics.
© 2016 Elsevier B.V.
- Accumulating priority
- First passage time
- Lévy driven queues
- Lévy processes
- Priority queues
ASJC Scopus subject areas
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics