Transient Analysis of a Queueing Systems with Cyber Disruptions and Degraded Service

This paper presents a single-server queueing model inspired by modern cloud computing and virtualized data center systems, where servers may encounter sudden cyber disruptions and workload degradation. Incoming user tasks arrive according to a Poisson process while the server operates in the primary service state. Service times in the primary service state and the fallback processing state are exponentially distributed under the First-Come-First-Serve discipline. Whenever the task queue becomes empty, the server enters a resource refresh phase before returning to full operational capacity. During the primary service state, disruptive cyber events occur randomly, forcing the system into the fallback processing state. At the moment of disruption, the task currently under execution is terminated, while the remaining queued tasks continue to receive service at a reduced processing speed. Once all pending tasks are completed in the fallback state, the server undergoes resource refresh and resumes normal operation. The system is modeled as a continuous-time Markov process, and probabilistic methods are used to formulate the governing equations. Probability generating functions, Laplace transform techniques, and the Matrix Geometric method are employed to derive transient and steady-state results together with important performance measures. Numerical studies are conducted to analyze the influence of cyber-event intensity, refresh mechanisms, and degraded processing efficiency on cloud system reliability and service performance.