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

Authors:
Tien Van Do;Dénes Papp;Ram Chakka;János Sztrik;Jinting Wang
Affiliations:
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
Venue:
International Journal of Advanced Intelligence Paradigms
Year:
2014

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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.