Fuzzy Parameterized Queueing Models with Applications to Service Optimization

Classical stochastic queueing models rely on precisely specified arrival and service parameters, an assumption that is often incompatible with service systems operating under incomplete information, measurement error, or linguistic assessments. In such environments, probabilistic descriptions alone may not adequately represent parameter uncertainty, leading to instability misclassification or suboptimal control decisions. This study formulates a queueing framework in which key system parameters, including arrival rates and service capacities, are represented as fuzzy numbers within a stochastic setting. The model integrates α–cut representations with standard queueing performance measures, enabling the derivation of stability conditions under imprecise parameterization. Sufficient conditions for system stability are established by examining fuzzy traffic intensity and its admissible realizations. Building on these results, an optimization problem is posed to minimize expected waiting-related costs subject to fuzzy stability and resource constraints. The formulation admits tractable solution procedures based on parametric decomposition across α–levels. A numerical illustration motivated by a hospital outpatient department demonstrates how fuzzy parameterization captures operational ambiguity in demand intensity and service efficiency, and how optimized staffing decisions differ from those obtained under crisp assumptions. The analysis shows that incorporating fuzziness leads to more robust performance assessments while preserving analytical transparency