A dual-regime impatience in Markovian batch arrival queueing system with disasters, working breakdowns and repair periods

Latency-sensitive service systems may experience customer abandonment during normal operation and degraded conditions caused by failures and repairs. Existing queueing models often overlook differences in customer impatience between these regimes. To address this gap, we develop a Markovian MX/M/c queueing model incorporating batch arrivals, disasters, working breakdowns, repair, Bernoulli feedback, and dual-regime impatience. We derive the stability condition, steady-state probabilities, and key performance measures using recursive and probability generating function approaches. An economic cost model is formulated, and a quadratic fit search method (QFSM) identifies cost-minimizing service-rate values under the considered settings. Numerical results show that higher arrival rates increase congestion and abandonment, while higher impatience rates reduce system size but also decrease customers served and profitability. Increasing servers reduces congestion but raises operating costs, whereas faster repair improves recovery and economic performance. These findings provide managerial insights for balancing service capacity and operating costs in failure-prone service systems.