Title: A study on M/G/1 retrial queueing system with three different types of customers under working vacation policy

Authors: P. Rajadurai

Addresses: Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA University, Kumbakonam – 612 001, Thanjavur, Tamilnadu, India

Abstract: This paper deals with a single server retrial queueing system with working vacations and vacation interruption. There are three different types of customers are considered, which are priority customers, ordinary customers and negative customers. The priority customers do not form any queue and have an exclusive preemptive priority to receive their services over ordinary customers. The negative customer is arriving during the service time of any positive customer, will remove the positive customer from the service. If the interrupted customer is an ordinary customer, he will leave the system. As soon as the orbit becomes empty at the time of service completion, the server goes for a working vacation. The server works at a lower speed during a working vacation period. Using the supplementary variable technique, the steady-state probability generating a function of the system and its orbit are found. Some numerical examples are presented.

Keywords: retrial queue; priority queue; negative customers; working vacations; supplementary variable technique.

DOI: 10.1504/IJMMNO.2018.094550

International Journal of Mathematical Modelling and Numerical Optimisation, 2018 Vol.8 No.4, pp.393 - 417

Received: 03 Aug 2017
Accepted: 18 Nov 2017
Published online: 06 Sep 2018 *

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