An M X /G(a,b)/1 Queueing System With Two Fluctuating Modes Of Service Under Bernoulli Vacation Schedule For Unreliable Server and Delaying Repair G. Ayyappan 1 , R. Supraja 2 1,2 Dept. of Mathematics, Pondicherry Engineering College, Puducherry, India. 1 ayyappan@pec.edu, 2 suprajaa11@gmail.com Abstract This paper deals with a batch arrival queueing system pre- pared with a single server providing service to a batch of cus- tomers with dissimilar service rate in two fluctuating modes of service. By using the supplementary variable technique, we de- rive the probability generating function of the number of cus- tomers in the queue at a random epoch under the steady state conditions. Performance measures like mean queue size has been obtained explicitly. Key Words: General bulk service, Two modes of service, Bernoulli vacation, Delay time, Repair time. AMS Subject Classification (2010): 60K25, 90B22, 68M20 1 Introduction A comprehensive study on batch service queue was initiated with the work of Bailey [3] . Some general bulk service results have discussed by Holman et al. [6]. Ayyappan and Shymala [1] analyzed a batch arrival single server with two stage heterogeneous service, Bernoulli International Journal of Pure and Applied Mathematics Volume 120 No. 8 2018, 49-57 ISSN: 1314-3395 (on-line version) url: http://www.acadpubl.eu/hub/ Special Issue http://www.acadpubl.eu/hub/ 49