Title: M/M/1 retrial queue with working vacations and negative customer arrivals

Authors: Tien Van Do; Dénes Papp; Ram Chakka; János Sztrik; Jinting Wang

Addresses: Department of Networked Systems and Services, Budapest University of Technology and Economics, H-1117, Magyar Tudósok körútja 2, Budapest, Hungary ' Department of Networked Systems and Services, Budapest University of Technology and Economics, H-1117, Magyar Tudósok körútja 2, Budapest, Hungary ' Department of Networked Systems and Services, Budapest University of Technology and Economics, H-1117, Magyar Tudósok körútja 2, Budapest, Hungary ' Faculty of Informatics, University of Debrecen, Egyetem tér 1, P. O. Box 12, 4010 Debrecen, Hungary ' Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, China

Abstract: The M/M/1 retrial queue with working vacations and negative customers is introduced. The arrival processes of positive customers and negative customers are Poisson. Upon the arrival of a positive customer, if the server is busy the customer would enter an orbit of infinite size and the orbital customers send their requests for service with a constant retrial rate. The single server takes an exponential working vacation once customers being served depart from the system and no customers are in the orbit. Arriving negative customers kill a batch of the positive customers waiting in the orbit randomly. Efficient methodology to compute the stationary distribution for this new queue is developed and presented.

Keywords: retrial queues; working vacations; negative customers; customer arrivals.

DOI: 10.1504/IJAIP.2014.059586

International Journal of Advanced Intelligence Paradigms, 2014 Vol.6 No.1, pp.52 - 65

Received: 01 Mar 2013
Accepted: 22 Aug 2013
Published online: 28 Jun 2014 *

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