2016/12/07 by Neal Master, Zhengyuan Zhou, Master, Neal +3
Business, Management and Accounting · Decision Sciences · #Advanced Queuing Theory Analysis #FOS: Computer and information sciences #FOS: Mathematics #Performance (cs.PF) #Probability (math.PR) #Probability and Risk Models #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1701.01328
openalex publication_date 2016/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.