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This paper proposes the nonparametric asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system, after perturbation of arrival distribution to evaluate the proximity of the complex GI/M/1 system, where GI is a unknown general distribution. The class of generalized gamma (GG) kernels is considered because of its several interesting properties and flexibility. A simulation for several models illustrates the performance of the GG asymmetric kernel estimators in the study of strong stability of the PH/M/1, by computing the variation distance and the stability error.

Asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system