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

Abstract

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 queue, working vacations, negative customersReference to this paper should be made as follows: Do, T.V, Papp, D., Chakka, R., Sztrik, J. He has participated and lead work packages in the COPERNICUS-ATMIN 1463, the FP4 ACTS AC310 ELISA, FP5 HELINET, FP6 CAPANINA projects funded by EC (where he acted as a work package leader). He led various projects on network planning and software implementations that results are directly used for industry such ATM & IP network planning software for Hungarian Telekom, GGSN tester for Nokia, performance testing program for the performance testing of the NOKIAs IMS product, automatic software testing framework for Nokia Siemens Networks. His research interests are queuing theory, telecommunication networks, cloud computing, performance evaluation and planning of ICT Systems.Denes Papp is a researcher in the Analysis, Design and Development of ICT systems (AddICT) Laboratory. He has participated in various software projects with NOKIA and Nokia Siemens Networks.

Analysis of a Discrete-Time Queueing Model with Disasters

“…For related work on discrete-time G-queues with negative customers, the reader is referred to [3,7,14,[16][17][18][19][20][21][22][23]. For work on continuous-time queueing models with negative customers and/or disasters, we refer to the bibliography in [24,25] and the more recent papers [26][27][28][29][30][31][32][33][34][35][36]. Additionally, somewhat related to this paper in the sense that customers may leave the system before their service is completed are queueing models with customer impatience or deadlines; we refer to [37] and the references therein for an overview of such models.…”

An Unreliable Batch Arrival G-Queue With Working Vacation, Vacation Interruption and Multi-Optional Services

“…Working vacation queues with negative arrivals find wide applicability in the working of computer networks, web servers, file transfer systems and email servers. Do et al [1] studied an M/M/1 retrial G-queue with working vacation. Further, using S VT (Supplementary Variable Technique), Rajadurai et al [6] examined the performance of an M/G/1 retrial queue with balking under working vacation policy.…”

Finite source retrial queues with two phase service

“…They derived some useful performance measures of the system such as the idle probability of the system, the mean number of customers in the retrial queue and the expected retrial time. Do et al (2014a) focused on a retrial queueing system with working vacations and negative customers are Poisson. But, when the customer population is of moderate size, it seems more appropriate that the retrial queueing systems should be studied as a system with finite source of customers.…”