Fluid Model to Calculate Active/Inactive Nodes in Computer Networks
摘要
In modern communication systems, it is common to find that nodes or users arrive in the system to remain active for a certain amount of time during which it will attempt to transmit a series of data packets to then leave. For instance, in VoIP systems, when a call is established, nodes become active and during specific periods will transmit (talking spurs when speaking in the line) and will remain inactive for other periods (silent spurs when listening to the interlocutor) and then leave the system when the call is over. This exact procedure occurs in Wireless Sensor Networks (WSNs) when nodes become active and begin sensing their surroundings, At this point, nodes attempt data packet transmissions when events occur or continuously transmitted to the sink node to then enter a low-energy consumption mode (sleep mode). These are just some examples of networks where this ON/OFF behavior is found, when during the ON period, there are multiple packet transmission attempts and in the OFF period, nodes usually enter a low energy consumption mode to save energy. In this work, we develop a fluid model to calculate the number of active and inactive nodes in communication systems. We propose a teletraffic analysis that considers arrivals of nodes, active time (session time), and ON/OFF activity processes for individual nodes. The system is simulated to verify the accuracy of the analytical results. Since many papers published in the literature consider a fixed number of users in the system, this analysis can be useful to estimate the number of active nodes when the system is in statistical equilibrium.