An Infinite Dimensional Model for a Many Server Priority Queue
Abstract
We consider a Markovian many server queueing system in which customers are preemptively scheduled according to exogenously assigned priority levels. The priority levels are randomly assigned from a continuous probability measure rather than a discrete one and hence, the queue is modeled by an infinite dimensional stochastic process. We analyze the equilibrium behavior of the system and provide several results. We derive the Radon-Nikodym derivative (with respect to Lebesgue measure) of the measure that describes the average distribution of customer priority levels in the system; we provide a formula for the expected sojourn time of a customer as a function of his priority level; and we provide a formula for the expected waiting time of a customer as a function of his priority level. We verify our theoretical analysis with discrete-event simulations. We discuss how each of our results generalizes previous work on infinite dimensional models for single server priority queues.
Cite
@article{arxiv.1701.01328,
title = {An Infinite Dimensional Model for a Many Server Priority Queue},
author = {Neal Master and Zhengyuan Zhou and Nicholas Bambos},
journal= {arXiv preprint arXiv:1701.01328},
year = {2017}
}
Comments
6 pages. arXiv admin note: substantial text overlap with arXiv:1609.07996