Bulk Arrival Retrial Queue with Unreliable Server and Priority Subscribers

⎯This paper is concerned with the analysis of unreliable server bulk arrival retrial queue with two class non-preemptive priority subscribers. The two types of subscribers arrive according to Poisson flow in which priority is assigned to class one, and class two subscribers are of non-priority type. The subscribers in each class arrive to the system in batches; the batch sizes follow the geometric process. If the server is free at the time of any batch arrivals, the subscriber of this batch begins to be served immediately and leave the system forever. The priority subscribers that find the server busy are queued and then are served in accordance with FCFS discipline. The arriving non-priority subscribers on finding the server busy cannot be queued and leave the service area and try their chance after some random time. If a subscriber is being served at the instant of the server failure, the service is interrupted and restarted after repair. The life time of the server is assumed to be exponentially distributed. The repair time and service time are also assumed to be i.i. d. general distributed. We obtain the condition of Ergodicity for such a queueing system. The analytical results for queue size distribution as well as some performance characteristics under steady state conditions by applying supplementary variable technique are derived. The waiting time distribution is also discussed for priority and non-priority subscribers. By taking illustration, computational results are provided to facilitate the sensitivity analysis. Keywords⎯Bulk arrival, Retrial queue, Non-preemptive priority, Unreliable server, Supplementary variables, Queue size, Waiting time. Biographical Notes⎯Madhu Jain is an Associate Professor of Mathematics in the Dr. BR Ambedkar University, Agra. She is a recipient of two Gold medals of the Agra University at MPhil level. There are more than 200 research publications in referred International/National journals and more than 20 books to her credit. She was a recipient of the Young Scientist Award and SERC visiting fellow the department of Science and Technology (DST), India and Career Award of University Grant Commission (UGC), India. She has successfully completed six sponsored major research project of DST, UGC and CSIR. Her current research interest includes the performance modeling, stochastic models, soft computing, bioinformatics, reliability, engineering and queueing theory. Charu Bhargava did her MSc and MPhil in Mathematics from Dr. BR Ambedkar University, Agra. Currently she is pursuing research for the degree of Ph.D. in the department of Mathematics, Institute of Basic Science, Agra under the supervision of Dr. Madhu Jain. Her research areas of interest include probability theory, stochastic models and queueing theory. She has participated and presented her research papers in seven International/National conferences. She was a recipient of Young Scientist Award for best paper presentation in “9th Conference of International Academy of Physical Sciences” held at Agra during Feb. 3-5, 2007. Several research articles jointly with Dr. Madhu Jain are being published in QTQM, Computers and Operations Research, Journal of KING ABDULAZIZ UNIVERSITY Engineering Sciences and OPSEARCH.