On the exact transient solution of fluid queue driven by a birth death process with specific rational rates and absorption

Abstract

Birth death processes with rational birth and death rates have been studied by Maki (1976). In this paper a fluid queue driven by a birth death process with infinite state space and absorption is studied where the birth and death rates are rational functions of linear polynomials. We obtain an explicit transient solution for the fluid queue model using continued fraction approach to solve the underlying system of partial differential equations. For specific value of the parameter the considered model reduces to the model discussed by Parthasarathy, and the results coincide. We also analyze the behavior of the fluid queue in a long run.

Analysis of Stationary Fluid Queue Driven by State-Dependent Birth-Death Process Subject to Catastrophes

“…We prove the above results by mathematical induction on m for every j . Now, using (15) in (12), we have…”

“…Konovalov [14] studied a more general / /1 GI GI fluid queueing model, where fluid flows out of the buffer at a constant rate. Kapoor and Dharmaraja [15] obtained an explicit transient solution of the fluid queue driven through birth death process via the continued fraction approach. Kapoor et al [16] studied the transient distribution of the buffer content of fluid queueing model driven by two distinct restricted state birth-death processes.…”

An Alleviation of Cloud Congestion Analysis of Fluid Retrial User on Matrix Analytic Method in IoT-based Application

“…In [11] encouraged Markov Modulated arrival process by obtaining steady state probabiliy distribution with phase type service and impatient customers. Reader can refer from [12], [13], [14] for further reference of fluid queues This paper makes two significant contributions. First, (i) To present a Matrix analytic method (MAM) based on data repetition phenomena to acquire the data from cloud data warehouse.…”