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

This paper investigates an infinite buffer capacity fluid queueing model driven by a state-dependent birth-death process prone to catastrophes. We employ the Laplace-Stieltjes transform and the continued fraction techniques to determine explicit expressions for the joint probability of the number of customers in the background queueing model and the content of the buffer in the steady state. The importance of the proposed system is that, in numerous practical situation, the service facility possesses defence mechanisms versus long waiting lines. The servers may increase their rate of service under the pressure of a large backlog of work. Therefore, it is of interest to discuss queueing systems taking into regard the state dependent nature of the systems. For example, the congestion control mechanisms deny the formation of long queue in computer and communication systems by controlling the transmission rates of packets based on the queue length (of packets) at source or destination. Numerical illustrations are added to uphold the theoretical results.