Abstract:

Based on practical application scenarios, a Markovian vacation queueing system with two types of breakdowns (working breakdowns and complete breakdowns) and two-stage service is considered, where breakdowns only occur in the first-stage service. During working breakdowns, customers are served at a reduced service rate. Once the system becomes empty, the server starts multiple vacations and resumes the first-stage service upon vacation completion. First, the steady-state probabilities of the system are derived by using the generating function method, and some performance measures are obtained. To validate the model’s reliability, Adaptive Neuro-Fuzzy Inference System (ANFIS) is employed for computational verification. For cost optimization, the fish school search (FSS) algorithm are utilized to identify optimal solutions. Then, based on the linear reward-cost structure, residual reward and social welfare functions are formulated to analyze customers' equilibrium joining probabilities and socially optimal probabilities. Finally, sensitivity analysis is conducted to illustrate the impacts of system parameters on customers' joining probabilities and optimal social welfare.

Key words: working breakdowns, two-stage service, vacation, joining probabilities, ANFIS