Title: On the time-dependent solution of fluid models driven by an M/M/1 queue using a probabilistic approach

Authors: S. Dharmaraja; Shruti Kapoor

Addresses: Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India ' Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India

Abstract: More study has been performed on the steady state analysis of fluid models. However, the transient analysis of fluid models has not been extensively carried due to complexity of the problem. This is because the system of conservation laws for which no closed form solution is available. The motivation behind this paper is to provide a new methodology to find transient distribution of buffer content for fluid models. In this paper, the time-dependent solution of a fluid model driven by an M/M/1 queue is derived using a simple probability approach. Finally, numerical results are illustration for the proposed approach.

Keywords: fluid models; M/M/1 queue; time-dependent.

DOI: 10.1504/IJOR.2023.128580

International Journal of Operational Research, 2023 Vol.46 No.1, pp.65 - 72

Received: 24 Oct 2019
Accepted: 09 Jan 2020
Published online: 26 Jan 2023 *