On The Single Server Retrial Queue With Balking

Abstract

We are concerned with the M/G/1 retrial queue with balking. The ergodicity condition is first investigated making use of classical mean drift criteria. The limiting distribution of the number of customers in the system is determined with the help of a recursive approach based on the theory of regenerative processes. Many closed form expressions are obtained when we reduce to the M/M/1 queue for some representative balking policies.

Résumé

Dans cet article on étudie une file d’attente du type M/G/1 avec rappels et “balking”. Premièrement on recherche la condition d’ergodicité en utilisant les critériums classiques des dérives moyennes. La distribution stationnaire du nombre de clients dans le système est déterminée avec l’aide d’une approximation recoursive basée sur la théorie des processus régénératifs. En outre, pour un modèle du type M/M/1 des expressions explicites sont obtenues.

Key Words:

• balking
• hypergeometric series, M/G/1 queue
• packet switching networks
• regenerative process
• retrials

Additional information

Notes on contributors

J.R. Artalejo

J.R. Artalejo is Professor in the Faculty of Mathematics at the University Complutense of Madrid. He received the Ph.D. degree in Mathematics from University Complutense of Madrid in 1991. He has published his research papers in a variety of journals such as Advances in Applied Probability, European Journal of Operational Research, Queueing Systems, OR Spektrum, etc. He is Associate Editor of Top and Guest Editor of Mathematical and Computer Modelling. His research interests are in Queueing Theory and Stochastic Modelling of Communication Systems.

M.J. Lopez-Herrero

M.J. Lopez-Herrero received her Ph.D. degree from the Autonoma University of Madrid in 1994. Since 1987, she has been teaching in the School of Statistics at the University Complutense of Madrid. Her research interests include Harmonic Analysis, Queueing Theory and Telecommunication Systems.