Economic and reliability analysis of discrete-time G-queue with multi-optional services and Bernoulli feedback

Cellular networks play a crucial role in modern telecommunications, supporting growing numbers of mobile users and various call types ranging from voice calls to multimedia data sessions. Efficient call handling is essential to ensure reliable and timely connections, optimal resource utilization, and a satisfactory Quality of Service (QoS). This study analyzes various call types in cellular networks using a discrete-time queueing model. Specifically, we investigate a discrete-time Geo/Geo/1 G-queue characterized by an unreliable server, k-optional services, and Bernoulli feedback mechanisms. Furthermore, within the framework of this queuing model, various call types are treated as positive customers, while virus attacks are considered negative customers. The arrival of a negative customer interrupts an ongoing service, leading to a server failure. Additionally, we assume that all arriving customers (positive) must undergo the First Essential Service (FES). After completing the FES, the server offers further services, allowing customers to either select one of the k-optional services, rejoin the queue for another FES, or leave the system if they do not wish to utilize additional services. Then, the entire system is modeled as a two-dimensional discrete-time Markov chain, and the matrix-geometric method is utilized to compute the steady-state probability vector, which is then employed to evaluate the numerical results of various performance metrics that depend on the queueing and reliability analysis. Finally, a cost model is established, and the Quasi-Newton method and Particle swarm optimization (PSO) technique are employed to achieve optimal operating conditions with minimal expected cost.