TY - JOUR

T1 - A 3-queue polling system with join the shortest-serve the longest policy

AU - Perel, Efrat

AU - Perel, Nir

AU - Yechiali, Uri

N1 - Publisher Copyright:
© 2022 Royal Dutch Mathematical Society (KWG)

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Gini index

KW - Join the shortest queue

KW - Matrix geometric

KW - Polling systems

KW - Probability generating functions

KW - Serve the longest queue

UR - http://www.scopus.com/inward/record.url?scp=85142182911&partnerID=8YFLogxK

U2 - 10.1016/j.indag.2022.11.001

DO - 10.1016/j.indag.2022.11.001

M3 - מאמר

AN - SCOPUS:85142182911

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

SN - 0019-3577

ER -