The current investigation proposes a novel queueing-theoretic approach by presenting an efficiency analysis and simultaneous comparison of unreliable server queues in a Markovian environment and their practical applications. Numerous sub-features of service interruptions, namely breakdown, partial server breakdown, and threshold-based recovery, are prioritized to navigate such a challenging queueing scenario. We utilize a queueing-theoretic approach to formulate mathematical models for each sub-feature, emphasizing the formulation of Chapman–Kolmogorov differential-difference equations to characterize their dynamics. The models are shown to be practically useful by deriving closed-form expressions for a variety of system performance metrics, and steady-state probability distributions are subsequently found by matrix solution techniques. Moreover, a thorough optimization, performance, and comparative analysis are carried out across the outcomes of every established model, providing insightful information for a thorough comprehension. Lastly, graphs and tables that provide management perspectives in a deeper understanding of the study’s significance are used to present the research findings.