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

Shruti Kapoor and Selvamuthu Dharmaraja

International Journal of Operational Research, 2020, vol. 37, issue 4, 562-578

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. (search for similar items in EconPapers)
Date: 2020
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