A flexible finite-state birth–death model for the number of active users in a cognitive network environment

Introduction Reliable handover mechanisms are vital for ensuring seamless connectivity in cognitive radio networks (CRNs). The challenge becomes more complex when the upper limit of allowable users fluctuates randomly and when arrival and service rates vary over time. To address these uncertainties, this study develops a dynamic modeling framework that captures the time-varying behavior of active users in CRNs. Method The system is formulated as a generalized birth–death queuing model with non-stationary transition rates and a flexible upper bound on the number of users. Arrival and service rates are modeled as functions of traffic intensity, reflecting peak and off-peak conditions. Transitions are restricted to adjacent states, and global balance equations are employed to establish the theoretical foundations of the model. Extensive simulations are conducted under multiple traffic scenarios to validate the model. Results The proposed flexible finite-state stochastic model effectively represents the temporal variations in user activity within CRNs. Simulation results confirm that the model accurately adapts to changing arrival and service rates and handles stochastic fluctuations in the system’s capacity limit. These findings demonstrate that the model can reliably predict system behavior under diverse network conditions. Discussions By capturing dynamic system variations and operational uncertainties, the developed model provides valuable insights for designing robust handover strategies in CRNs. Its ability to characterize real-world traffic patterns makes it a useful analytical tool for future cognitive communication systems. The work lays a foundation for optimizing device-level handover decisions and enhancing network reliability in environments with unpredictable user behavior.