2023/11/02 by Josef Zuk, Zuk, Josef, David Kirszenblat +1
Business, Management and Accounting · Decision Sciences · #60J74 (Secondary) #90B22 (Primary) 60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2311.01641
openalex publication_date 2023/11/02 · openalex created_date 2023/11/07 · openalex updated_date 2026/07/28
Explicit results are obtained using simple and exact methods for the joint queue-length distribution of the M/M/c queue with an arbitrary number of non-preemptive priority levels. This work is the first to provide explicit results for the joint probability generating function and joint probability mass function for a general number of priority levels. A fixed-point iteration is developed for the stationary balance equations, which enables direct computation of the joint queue-length distribution. A multi-variate probability generating function is also derived, from which the joint probability mass function can be computed by means of a multi-dimensional fast Fourier transform method.