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

Chandrasekaran V M

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Saravanarajan M C

Rajadurai P

Fulltext

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.

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VIT University

Ain Shams Engineering Journal

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

In this paper, we discuss about the steady state behaviour of M/G/1 retrial queueing system with two phases of services and immediate feedbacks under working vacation policy where the regular busy server is affected due to the arrival of negative customers. Upon arrival if the customer finds the server busy, breakdown or on working vacation it enters an orbit; otherwise the customer enters into the service area immediately. After service completion, the customer is allowed to make finite number of immediate feedback. The feedback service also consists of two phases. At the service completion epoch of a positive customer, if the orbit is empty the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. Using the supplementary variable technique, we found out the steady state probability generating function for the system and in orbit. System performance measures and reliability measures are discussed. Finally, some numerical examples are presented to validate the analyticalresults. © Published under licence by IOP Publishing Ltd.

IOP Conference Series: Materials Science and Engineering

A study on M/G/1 retrial G - queue with two phases of service, immediate feedback and working vacations

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

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.

International Journal of Mathematics in Operational Research

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

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.

Analysis of M[X]/G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown

This paper deals with the steady state analysis of batch arrival retrial queueing system with two types of service under modified vacation policy, where each type consists of an optional re-service. An arriving batch may balk the system at some particular times. After the completion of each types of service the customers may re-service of the same type without joining the orbit or may leave the system. If the orbit is empty at the service completion of each types of service, the server takes at most J vacations until at least one customer is received in the orbit when the server returns from a vacation. Busy server may breakdown at any instance and the service channel will fail for a short interval of time. The steady state probability generating function for system/orbit size is obtained by using the supplementary variable method. Some system performance measures and numerical illustrations are discussed. © 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

Journal	Data powered by TypesetAin Shams Engineering Journal
Publisher	Data powered by TypesetElsevier BV
ISSN	2090-4479
Open Access	Yes