In steady state, a batch arrival feedback retrial queue with negative customers has been discussed. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them join into the orbit/retrial group, where the server provides two essential phases of service to each positive customer. The negative customer, arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters into the orbit with probability θ or leaves the system with probability 1-θ. The busy server may breakdown at any instant and the service channel will fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Numerical illustrations are analysed to see the effect of system parameters. © 2015 Inderscience Enterprises Ltd.

Chandrasekaran V M

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Saravanarajan M C

Rajadurai P

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

&nbsp;

&nbsp;

VIT University

Steady state analysis of batch arrival feedback retrial queue with two phases of service, negative customers, Bernoulli vacation and server breakdown

International Journal of Mathematics in Operational Research

In this paper, we consider a single server retrial queueing system with working vacations. Further vacation interruption is considering with the regular busy server is subjected to breakdown due to the arrival of negative customers. When the orbit becomes empty at the time of service completion for a positive customer, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. If there are customers in the system at the end of each vacation, the server becomes idle and ready for serving new arrivals with probability p (single WV) or it remains on vacation with probability q (multiple WVs). By using the supplementary variable technique, we found out the steady state probability generating function for the system and its orbit. System performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented. © 2016 Faculty of Engineering, Ain Shams University

Fulltext

Ain Shams Engineering Journal

Analysis of an unreliable retrial G-queue with working vacations and vacation interruption under Bernoulli schedule

In this paper, we consider a single server feedback retrial queueing system with multiple working vacations and vacation interruption. An arriving customer may balk the system at some particular times. As soon as orbit becomes empty at regular service completion instant, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. After completion of regular service, the unsatisfied customer may rejoin into the orbit to get another service as feedback customer. The normal busy server may get to breakdown and the service channel will fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented. © 2017 Faculty of Engineering, Alexandria University

Alexandria Engineering Journal

A study on M/G/1 feedback retrial queue with subject to server breakdown and repair under multiple working vacation policy

This article discusses the concepts of preemptive priority retrial queue with two-phase service, feedback, and Bernoulli vacation for an unreliable server, which consists of breakdown period. The queue involves two types of customers, known as priority and ordinary customers. The server provides first essential service and second essential service to the arriving customers or customers from the orbit. The server takes Bernoulli vacation, when an orbit becomes empty. The supplementary variable technique is used to obtain the steady-state probability generating functions for the system/orbit and some important system performance measures. © 2018, Springer Nature Switzerland AG.

Trends in Mathematics Advances in Algebra and Analysis

Steady-State Analysis of Unreliable Preemptive Priority Retrial Queue with Feedback and Two-Phase Service Under Bernoulli Vacation

This paper concerned with performance analysis of single server preemptive priority retrial queue with a single vacation where two types of customers are considered and they are called priority customers and ordinary customers. The ordinary customers arrive in batch into the system. The priority customers do not form any queue. After the completion of regular service, the customers may demand re-service for the previous service without joining the orbit or may leave the system. As soon as the system is empty, the server goes for vacation and the regular busy server can be subjected to breakdown. By using the supplementary variable technique, we obtain the steady-state probability generating functions for the system/orbit size. Some important system performance measures and the stochastic decomposition are discussed. Finally, numerical examples are presented to visualize the effect of parameters on system performance measures. © Published under licence by IOP Publishing Ltd.

IOP Conference Series: Materials Science and Engineering

Analysis on preemptive priority retrial queue with two types of customers, balking, optional re-service, single vacation and service interruption

In this paper, we consider a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers. Any arriving batch of positive customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. Arriving positive customers may balk (or renege) the system at particular times. After completion of service the unsatisfied positive customer may rejoin into the orbit to get another regular service as feedback customer. The server takes Bernoulli vacation after service completion of positive customers. After completion of service (if the server is not taking vacation), repair or vacation the server searches for the customers in the orbit or remains idle. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some system performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented. © 2015, Operational Research Society of India.

OPSEARCH

Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule

Many choices are available to the practitioner of restorative dentistry for children. With the introduction of several new classes of restorative materials in recent years, some confusion has been created about what these materials are, making it difficult to identify their appropriate clinical use. This paper reviews glass-ionomer materials, resin-modified (reinforced) glass ionomers, compomers, and composite resins for the practitioner. Definitions of these materials, a general description of their contents, and usage-selection criteria are provided. Although more choices for tooth restoration can make the selection of the right material more difficult, a better understanding of the components and the strengths and weaknesses of each category of materials offers the opportunity to select the right material for the right situation.

Journal	International Journal of Mathematics in Operational Research
Publisher	Inderscience Publishers
ISSN	1757-5850
Open Access	0