Inference of a Multi-server Queue Using External Observations

Since the autocorrelated arrivals and services complicate queue analysis, numerous modeling and analysis methods for the autocorrelated cases have been developed. This study aims to overcome the limits of the existing methods in some situations with a time-dependent structure in arrival or service process and trouble to observe the internal operations. With only external observations, the proposed method identifies the internal operation of a multi-server queue via a non-parametric approach even when the service times are autocorrelated. The efficiency and demonstration of this suggested inference method is measured by queue delays and service times of each customer. Mathematical proof and numerical examples are provided to verify the proposed inference method.