Steady State Analysis of an M/G/1 Queue with Repeated Attempts and Two-Phase Service

Abstract

This paper examines the steady state behavior of an M/G/1 queue with repeated attempts in which the server may provide an additional second phase of service. This model generalizes both the classical M/G/1 retrial queue and the M/G/1 queue with classical waiting line and second optional service. We carry out an extensive stationary analysis of the system, including existence of stationary regime, embedded Markov chain, steady state distribution of the server state and the number of customers in the retrial group, stochastic decomposition and calculation of the first moments.

Key Words:

• Retrial queues
• stationary distribution
• stochastic decomposition
• two-phase service

Additional information

Notes on contributors

J.R. Artalejo

Jesus Artalejo Professor of the Faculty of Mathematics at the Complutense University of Madrid. He received his Ph. D. degree in Mathematics from Complutense University of Madrid in 1991. He have published research papers in a variety of journals on Applied Probability, Operations Research and related fields. He is an Associate Editor of Asia-Pacific Journal of Operational Research, Computers and Operations Research, Journal of Applied Mathematics and Stochastic Analysis, Quality Technology & Quantitative Management, Queueing Systems, Revista Matemática Complutense, Statistics and Operations Research Transactions and Top, and has been Guest Editor of Annals of Operations Research and Mathematical and Computer Modeling. His main research interests concern with Queueing Theory and Stochastic Modeling of Communication Systems.

G. Choudhury

Gautam Choudhury Assistant Professor in Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Guwahati, Assam, India. He obtained his M.Sc. and Ph.D. in Statistics from Gauhati University, Guwahati, Assam, India. He has numerous publications in a variety of Journals of Statistics, Mathematics and Operations Research. His areas of interest are Queueing Theory, Applied Stochastic Process and Stochastic Modeling of Communication Systems. He is an Associate Editor of Far East Journal of Theoretical Statistics.