A fluid queue modulated by two independent birth–death processes

We present a fluid queue model driven by two independent finite state birth–death processes with the objective to study the buffer occupancy distribution in any intermediate node in a communication network. In a communication network, at any node, the arrival and service of the packets are with variable rates. To model this scenario we develop a fluid queue with an infinite capacity buffer which receives fluid at variable rate and also releases fluid at variable rates. Because of variable inflow and outflow rates of the fluid, the proposed fluid queue is driven by the current states of two independent finite state birth–death processes evolving in the background which on merging give rise to a continuous time Markov chain which is not a birth–death process. Using the fluid queue model, we obtain the steady-state distribution of the buffer occupancy at any intermediate node during packet transmission in a communication network. As a special case, we consider a wireless network based on the IEEE 802.11 standard. We present the buffer occupancy distribution at any intermediate node in closed form with a numerical illustration. Along with buffer occupancy distribution, we also obtain various performance measures such as expected buffer content, average throughput, server utilization and mean delay which are relevant to packet transmission in such a communication network. Finally, we present numerical results to illustrate the feasibility of the proposed model. The results are in accordance with the expected behavior of these performance measures.