International Journal of Mathematics Trends and Technology (IJMTT)- Special Issue ICRMIT March 2018 ISSN: 2231-5373 http://www.ijmttjournal.org Page 45 Unreliable Batch Arrival Retrial G-queue with Fluctuating Modes of Service, Preemptive Priority and Orbital Search K. Kirupa Dr. K. Udaya Chandrika Coimbatore, TamilNadu, India Professor and Head Avinashilingam Institute for Home Science and Higher Education for Women Coimbatore,Tamilnadu,India Abstract — In this paper, single server retrial queueing system with two types of customers is analyzed. The server provides M fluctuating modes of service. If the server is free upon the arrival of a batch, one of the customers in the batch receives service immediately and the rest join the orbit. If the server is busy, one of the customers in the arriving batch interrupts the customer in service to commence his own service. The breakdown of the server due to the arrival of a negative customer and an unpredictable breakdown are two different types of system failure. The repair of the failed server due to negative arrival starts after a random amount of time whereas repair due to active breakdown starts instantaneously. If the server is idle in non-empty system, then the server may search for customers in the orbit. Retrial time, service time, delay time and repair time are assumed to be arbitrarily distributed. Using generating functions technique, expressions of the system performance measures are obtained. Stochastic decomposition property and special cases are studied. Finally the effects of several parameters on system measures are shown numerically. Keywords— Retrial queue, positive customers, negative customers, M modes of service, priority, server breakdown, delayed repair and orbital search. I. INTRODUCTION Retrial queueing systems are characterized by the feature that a customer who cannot receive service leaves the service area but after some random delay returns to the system again to request service. In recent years, interest is growing in queues with negative customers due to their applications in the telecommunication system, neutral networks, multiprocessor computer systems and manufacturing systems. The named G-queue has been adopted for the queue with negative customers in acknowledgement of Gelenbe [7] who first introduced this type of queue. A detailed survey on queueing systems with negative arrivals can be found in Gelenbe [8-10]. Liu et al. [11] obtained the steady state solution for both queueing measures and reliability quantities of an unreliable M/G/1 retrial G-queue with preemptive resume and feedback under N- policy. Aissani [1] obtained the generating function of the number of primary customers in the stationary regime of an M/G/1 retrial queue with negative arrivals and server breakdown. Peng et al. [14] considered M/G/1 retrial G-queue with preemptive resume priority and collisions subject to server breakdowns and repairs and obtained the performance measures. Gao and Wang [6] analysed an M/G/1 – G queue with orbital search and non-persistent customers. Rajadurai et al. [15] studied an M X /G/1 unreliable retrial G-queue with orbital search, feedback and Bernoulli vacation. In the retrial setup, each service is preceded and followed by the server’s idle time because of the ignorance of the status of the server and orbital customers by each other. Server’s idle time is reduced by the introduction of search of orbital customers. Search for orbital customers was introduced by Neuts et al. [13] where the authors examined classical queue with search for customers immediately on termination of a service. Artalejo et al. [3] considered a retrial queue with orbital search. Dudin et al. [5] extended the model to a batch arrival retrial queue and performed the steady state analysis of the queueing system. Sumitha and Udaya Chandrika [17] discussed a single server batch arrival retrial queueing system with additional optional service and orbital search. Sumitha and Udaya Chandrika [18] investigated a repairable M/G/1 retrial queue with Bernoulli vacation and orbital search. Deepak et al. [4] considered a retrial model in which at each service completion epoch, two different search mechanisms are switched on to bring the orbital customers to service. Most of the single server queueing models assume that the server provides service to all customers with the same mean service rate. This is not possible in the real life situation. Baruah et al. [3] studied the behaviour of a batch arrival queueing system equipped with a single server providing