This study addresses the challenge of modeling uncertainty and indeterminacy in queueing systems, which classical queueing models fail to capture due to their dependence on precisely defined parameters. By reformulating conventional queueing models through a neutrosophic lens, the study provides a unified mechanism for quantifying uncertainty and assessing its influence on performance metrics. Four queue configurations,(M/M/1; \(\infty\) /FIFO, M/M/1;k/FIFO, M/M/c; \(\infty\) /FIFO and M/M/c;k/FIFO) are extended using trapezoidal neutrosophic fuzzy numbers for arrival and service rates, integrating truth, indeterminacy, and falsity dimensions of system behavior. The ( \(\alpha ,\beta ,\gamma\) ) - cut approach and Zadeh’s extension principle are employed to transform these neutrosophic models into their parametric equivalents, allowing analytical evaluation through neutrosophic parametric programming. A Response Surface Methodology (RSM) based sensitivity analysis quantifies the impact of key parameters arrival rate midpoint, service rate midpoint, spread, and indeterminacy factor on the system response. The findings reveal that the arrival rate midpoint exerts the greatest influence on uncertainty width, while the service rate midpoint stabilizes performance variability, confirming the robustness of the proposed models. The neutrosophic framework enhances flexibility and predictive accuracy by providing bounded performance estimates rather than deterministic values. Its real world applicability is demonstrated through potential use in modeling Network Interface Cards (NICs) and cloud computing systems, where traffic fluctuations and incomplete information dominate, thereby bridging theoretical analysis with complex operational realities.
