2022/04/18 by Efrat Perel, Perel, Efrat, Nir Perel +3
Business, Management and Accounting · Health Professions · Mathematics · #Advanced Queuing Theory Analysis #Combinatorics #Computer network #Computer science #FOS: Mathematics #Fork–join queue #Healthcare Operations and Scheduling Optimization #Join (topology) #Mathematics #Polling #Probability (math.PR) #Queue #Queue management system #Queueing theory
paper · pdf · doi:10.48550/arxiv.2204.08346
openalex publication_date 2022/04/18 · openalex created_date 2022/04/26 · openalex updated_date 2026/08/06
In 1987, J.W. Cohen analyzed the so-called Serve the Longest Queue (SLQ) queueing system, where a single server attends two non-symmetric M/G/1-type queues, exercising a non-preemptive priority switching policy. Cohen further analyzed in 1998 a non-symmetric 2-queue Markovian system, where newly arriving customers follow the Join the Shortest Queue (JSQ) discipline. The current paper generalizes and extends Cohen's works by studying a combined JSQ-SLQ model, and by broadening the scope of analysis to a non-symmetric 3-queue system, where arriving customers follow the JSQ strategy and a single server exercises the preemptive priority SLQ discipline. The system states' multi-dimensional probability distribution function is derived while applying a non-conventional representation of the underlying process's state-space. The analysis combines both Probability Generating Functions and Matrix Geometric methodologies. It is shown that the joint JSQ-SLQ operating policy achieves extremely well the goal of balancing between queue sizes. This is emphasized when calculating the Gini Index associated with the differences between mean queue sizes: the value of the coefficient is close to zero. Extensive numerical results are presented.