Title: Steady state analysis of fluid queues driven by birth death processes with rational rates

Authors: Shruti Kapoor; Selvamuthu Dharmaraja

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: Birth death processes with rational birth death rates have been studied by Maki (1976). This paper analyses the steady state behaviour of a fluid queue driven by a finite birth death process with rational birth and death rates. Two specific models are considered and closed form solutions are obtained for the equilibrium distribution of the buffer occupancy by finding the explicit eigenvalues of the underlying tridiagonal matrix. Numerical illustration is presented for different values of the size of the state space of the background process and for different values of the parameter involved.

Keywords: fluid queue; stationary distribution; eigenvalues; tridiagonal matrices.

DOI: 10.1504/IJOR.2020.105768

International Journal of Operational Research, 2020 Vol.37 No.4, pp.562 - 578

Received: 24 Oct 2016
Accepted: 09 May 2017
Published online: 13 Mar 2020 *

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