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Queueing systems are modeled by equations which depend on a large number of input parameters. In practice, significant uncertainty is associated with estimates of these parameters, and this uncertainty must be considered in the analysis of the model. The objective of this paper is to propose a sensitivity analysis approach for a queueing model, presenting parameters that follow a Gaussian distribution. The approach consists in decomposing the output of the model (stationary distribution of the model) into a polynomial chaos. The sensitivity indices, allowing to quantify the contribution of each parameter to the variance of the output, are obtained directly from the coefficients of decomposition. The proposed approach is then applied to M/G/1/N queueing model. The most influential parameters are highlighted. Finally several numerical and data examples are sketched out to illustrate the accuracy of the proposed method and compare them with Monte Carlo simulation. The results of this work will be useful to practitioners in various fields of theoretical and applied sciences. [ABSTRACT FROM AUTHOR]