A Quorum Queueing System with a Random Setup Time under N-policy and with Bernoulli Vacation Schedule

Abstract

We aim in this paper at designing an optimal management policy for a bulk service queueing system with random set-up time under Bernoulli vacation schedule and N-policy. We first study the discrete time parameter and continuous time parameter stochastic processes and derive all the quantities required to build a linear cost structure. Then an algorithm is suggested to determine the optimal management policy. An illustrative example is presented to show how to implement this policy and a sensitivity analysis is conducted to determine the effect of the system parameters.

Key Words:

• Bernoulli schedule
• N-policy
• optimal control
• queue
• quorum
• set-up
• vacation

Additional information

Notes on contributors

Lotfi Tadj

Lotfi Tadj is a Professor of Operations Research in the Department of Statistics and Operations Research, King Saud University, Riyadh, Saudi Arabia. His research interests include the optimal control of queueing and inventory systems. He is an editorial board member of the Journal of Probability and Statistical Science. He has numerous publications in journals of mathematics, statistics, and operations research.

Gautam Choudhury

Gautam Choudhury is an Assistant Profesor in the Mathematical Science Division, Institute of Advanced Study in Science and Technology, Paschim Boragoan, Guwahati-781035, Assam, India. His areas of interests are queueing theory, stochastic modelling, and applied stochastic process. He is an editorial board member of the Far East Journal cof Theoretical Statistics. He has numerous publications in journals of mathematics, statistics, and operations research.

Chakib Tadj

Chakib Tadj is a Professor in the Department of Electrical Engineering, at École de Technologie Supérieure (ETS), University of Quebec at Montreal, Canada. He is a Member of the LATIS Laboratory (LAboratoire du Traitement de lInformation et des Signaux) at ETS. His main research interests include signal processing, ubiquitous/pervasive computing and intelligence, and multimodal systems.