Moment Inequalities For A Class Of Single Server Queues

Abstract

The limiting behaviour of the single server queue is discussed for a general class of inter-arrival distribution functions of practical interest. New upper and lower bounds are derived for the first order measures (expected waiting time, queue size, etc.). Also presented are some numerical results on the influence of the inter-arrival and service time third moments upon the first- and second-order measures.

Résumé

On examine le comportement limite de la file d’attente à canal unique pour une classe générate de durees d’attente. De nouvelles bornes supérieures et inférieures pour les mesures de premier ordre (espérance du temps d’attente, de la longueur de la file d’attente, etc.) sont obtenues. On présente également certains résultats numériques sur l’influence des troisiémes moments des durées d’attente et de service sur les mesures du premier et deuxiéme ordre.

Additional information

Notes on contributors

Izzet Sahin

IzzET SAHIN is an Associate Professor of Operations Research in the Faculty of Management Sciences at the University of Ottawa; he has recently been named the Chairman of the Department of Operations Research and Planning. He holds graduate degrees in Engineering and Management Science and a PH D degree in Operations Research from Case Institute of Technology. His research interests are in the area of Probabilistic Models in Management; he has published several papers in Applied Probability, Operations Research, Management Science and International Economic Review.

Stylianos Perrakis

STYLIANOS PERRAKIS is an Associate Professor of Managerial Economics and Operations Research in the Faculty of Management Sciences, University of Ottawa. He served as Chairman of the Department of Operations Research and Planning during 1975-6. He holds a diploma in Engineering from the National Technical University of Athens, Greece, and an MS and PH D (1970) in Industrial Engineering and Operations Research from the University of California at Berkeley. His research and teaching interests are in the areas of Mathematical Economics and Finance. He is the author of many articles published in, among others, Management Science, International Economic Review, Journal of Financial and Quantitative Analysis, and American Economic Review.