2025/10/21 by Nicos Georgiou, Enrico Scalas, Georgiou, Nicos +3
Business, Management and Accounting · Decision Sciences · Engineering · #60B51 #60F17 #60G55 #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Reliability and Maintenance Optimization
paper · pdf · doi:10.48550/arxiv.2510.18461
openalex publication_date 2025/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index α∈ (0,1] and the service completions are triggered by an independent fractional Poisson process of index β∈ (0,1]. Each of the customers arriving is assigned at random to one of the priority classes. This assignment is independent of the rest of the system and follows a fixed probability distribution. Using a time-change representation of a fractional Poisson process, we first give a multinomial thinning decomposition: the total number of arrivals in each class are independent standard Poisson processes of appropriate intensities, time-changed by a common independent random clock that is the inverse of an α-stable subordinator. This yields a process-level law of large numbers and a functional central limit theorem for the process of arrivals. For the queueing system itself, we identify process-level scaling limits for the cumulative and individual queue lengths of the classes. We also prove that the queue gets empty infinitely often when α≤ β, which does include the critical case α= β. A final example shows how the model can be extended to a continuum of classes.