Waiting-Time Moments In The Queueing System GI/M^a,b/1

Abstract

This paper deals with the queueing system GI/M^a,b/1 Expressions are derived for the moments of the steady-state waiting time (in queue) and the moments of the conditional waiting time (in queue) of customers who are mth in their batch. Sample numerical results are presented for the first two moments of the former. The results demonstrate that models of this kind become relatively insensitive to the coefficient of variation of the interarrival-time distribution as the capacity increases. They permit the quantitative assessment of waiting-time costs over a wide range of traffic intensity, quorum, and capacity.

Résumé

Cet article étudie le modèle de files d’attente GI/M^a,b/1 On y trouve les expressions pour les moments du temps d’attente en équilibre (dans la file) et les moments du temps d’attente conditionnel (dans la file) des clients qui sont m ième dans leur groupe. Des échantillons de résultats numériques sont présentés pour les deux pretniers moments de la première variable ci-haut. Les résultats démontrent que, quand la capacité augmente les modeles de ce genre deviennent relativement indépendants du coefficient de variation de la distribution du temps entre les arrivées. Ils permettent une évaluation quantitative des coûts du temps d’attente, pour diverses valeurs d’intensité de la circulation, de quorum et de capacité.

Additional information

Notes on contributors

B.R. Madill

B.R. MADILL received an Honours B SC degree in mathematics and physics from the Royal Military College of Canada, Kingston, Ontario in 1976. He worked in the fields of communications research and radar until 1980, when he returned to RMC and obtained an M SC degree in Operations Research. Currently Captain Madill lectures in the Department of Mathematics and Computer Science at RMC and is a PH D student in Management Science at Queen's University.

M.L. Chaudhry

M.L. CHAUDHRY is a Professor in the Department of Mathematics and Computer Science at the Royal Military College of Canada, Kingston, Ontario. He was a senior post-doctoral Fellow at the University of Toronto during 1966–7. Since receiving his PHD in Operations Research from Kurukshetra University, India, he has held visiting appointments at several institutes of learning. He has contributed articles to numerous international journals and is a member of several professional societies. He recently published (co-authored with J.G.C. Templeton) a book titled A First Course in Bulk Queues (Wiley). Included among Professor Chaudhry's current interests are Applied Probability and Stochastic processes.