Quantification of system resilience through stress testing using a predictive analysis of departure dynamics in a $$M^X/G/1/N$$ queue with multiple vacation policy

The study investigates the departure counting process in a finite-buffer queueing system with batch arrivals and multiple vacation policy, focusing on quantifying system resilience through stress testing and predictive analysis. A representation for the mixed double transform of the number of departures up to a fixed time moment is obtained in explicit form by applying an analytic approach based on integral equations and linear algebra. We perform a comparative analysis of numerical calculations and simulations made in OMNeT++ Discrete Event Simulator. The attached numerical study aims to understand how the queueing system copes under challenging conditions, examining the impact of various system parameters on the behaviour of the mean number of packets processed within a fixed time frame. Utilizing numerical experiments, the study analyzes the influence of vacation duration, initial buffer state, arrival intensity, and processing rate on the departure process. This enables the understanding of system recovery dynamics, particularly in how critical infrastructures can be optimized for resilience against disruptions. Results reveal significant dependencies between these parameters and the transient behaviour of the queueing system. Notably, the service speed parameter demonstrates the most substantial influence on the mean number of processed packets, followed by the arrival rate. Conversely, variations in vacation duration and initial packet count exhibit comparatively minor effects on system behaviour. Overall, the findings provide valuable insights into the dynamics of departure processes in finite-buffer queue systems with batch arrivals and multiple vacation policies, offering implications for system optimization, performance enhancement strategies, and resilience assessment in the face of potential system failures or disasters.