Int. J. Mathematics in Operational Research, Vol. 16, No. 2, 2020 217 Transient analysis of multi-server Markovian queueing system with synchronous multiple working vacations and impatience of customers P. Vijaya Laxmi* and T. Wondewosen Kassahun Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam – 530 003, India Email: vijaya iit2003@yahoo.co.in Email: wondukass@gmail.com *Corresponding author Abstract: In this paper, we study an infinite capacity multi-server Markovian queue with synchronous multiple working vacations, balking and reneging. It is assumed that customers may balk and/or renege with some probability if all the c servers are busy serving customers either during the regular busy period or working vacation period. The reneging times follow an exponential distribution. The system is modeled by a quasi-birth-death process and the transient-state probabilities of the model are obtained in the Laplace domain using matrix geometric method. Keywords: multiple working vacations; balking; reneging; transient-state probabilities; matrix geometric method; Laplace transform. Reference to this paper should be made as follows: Laxmi, P.V. and Kassahun, T.W. (2020) ‘Transient analysis of multi-server Markovian queueing system with synchronous multiple working vacations and impatience of customers’, Int. J. Mathematics in Operational Research, Vol. 16, No. 2, pp.217–237. Biographical notes: P. Vijaya Laxmi is an Assistant Professor in the Department of Applied Mathematics, Andhra University, Visakhapatnam, India. She received her MSc and PhD from the Indian Institute of Technology, Kharagpur, India. Her main areas of research interest are continuous and discrete-time queueing models and their applications. She has publications in various journals like Operations Research Letters, Queueing Systems, Applied Mathematical Modelling, International Journal of Applied Decision Sciences, Journal of Industrial and Management Optimization (JIMO), etc. T. Wondewosen Kassahun is a Doctoral student in the Department of Applied Mathematics, Andhra University, India. He received his MSc in 2010 from the Addis Ababa University, Ethiopia. His research interests are stochastic modelling, queueing theory and its applications. Copyright © 2020 Inderscience Enterprises Ltd.