Title: A single server Markovian differentiated working vacation queue with server breakdown

Authors: V. Karthick; V. Suvitha; Rathinasabapathy Kalyanaraman

Addresses: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603203, Tamilnadu, India ' Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603203, Tamilnadu, India ' Department of Mathematics, Annamalai University, Annamalainagar-608002, Tamilnadu, India

Abstract: A single server Markovian queue with server breakdown has been considered here. In addition, the server goes on two types of vacation namely type-I and type-II. Type-I vacation is taken after the busy period of non-zero duration and type-II vacation occurs, at the completion of type-I vacation. When there are no customers in the system, both type-I and type-II vacations are working vacations. Also, on type-I vacation, the server may breakdown, and immediately the repair takes place. We analysed it as a quasi-birth-and-death (QBD) process, and using the matrix geometric method, the steady-state probability vector of the number of people in the queue and the stability conditions were produced. There are some system performance measures found. The effects of various parameters on the system performance measures are illustrated numerically.

Keywords: single server; differentiated vacation; breakdown; repair; QBD process.

DOI: 10.1504/IJMOR.2024.136862

International Journal of Mathematics in Operational Research, 2024 Vol.27 No.1, pp.105 - 120

Received: 14 Jul 2022
Accepted: 24 Nov 2022
Published online: 23 Feb 2024 *