Workload Resets and Vacation-Driven Congestion in Continuous-Flow Service Systems: A Steady-State Fluid Queueing Analysis under Catastrophe

This paper presents an analytical study of a fluid queueing model driven by an M/M/1 system with homogeneous exponential server vacations and catastrophic reset events. The novelty of the proposed model lies in the integration of vacation dynamics and instantaneous catastrophic clearing within a continuous-flow framework. The model represents high-rate service environments in which workload accumulates continuously while the server becomes intermittently unavailable due to maintenance, energy-saving modes, or unexpected interruptions. Arrivals follow a Poisson process, and service times are exponentially distributed. The steady-state behavior of the system is analyzed by formulating and solving a set of governing equations using Laplace transform techniques, reducing the problem to a quadratic equation. This approach yields closed-form expressions for the stationary buffer-content distribution and the mean buffer content. The results reveal that the average congestion is insensitive to the vacation parameter, whereas the catastrophe rate and net input drift significantly influence system performance. Numerical experiments are conducted to illustrate the impact of system parameters on buffer occupancy, validating the analytical findings. The results provide practical insights for buffer dimensioning, congestion control, and resilience evaluation in modern data-intensive service systems such as cloud computing, communication networks, and automated production environments.