Title: Transient analysis of various vacation interruption policies in a Markovian queue with differentiated multiple vacations
Authors: A. Azhagappan; T. Deepa
Addresses: Department of Mathematics, St. Anne's College of Engineering and Technology, Anna University, Panruti, Tamil Nadu – 607110, India ' Department of Mathematics, Idhaya College of Arts and Science for Women, Pondicherry University, Pakkamudayanpet, Puducherry – 605008, India
Abstract: Two different types of interruptions (partial and complete) of server's vacation are discussed in this research work along with two different types of vacations (types 1 and 2). The transient analysis of an M / M / 1 queueing model with differentiated multiple vacations, partial and complete interruption of vacations is carried out. Two types of vacations are studied in this research work. Type 1 vacation is taken after serving all the customers in the system exhaustively. Type 2 vacation is resumed after returning from type 1 vacation and finding the empty system. Partial interruption is the one in which the interruption happens only in type 2 vacation whereas complete interruption can occur in both types 1 and 2 vacations. The system size distributions are derived using generating function and Laplace transforms under transient case. The average and variance are also obtained. Further, numerical simulations are presented.
Keywords: the M / M / 1 queue; differentiated multiple vacations; partial and complete interruption of vacations; transient probabilities.
International Journal of Operational Research, 2022 Vol.45 No.4, pp.492 - 510
Received: 24 Aug 2019
Accepted: 01 Feb 2020
Published online: 20 Jan 2023 *