Analyzing an <i>M/G/1</i> Double Orbit Retrial Queue with the Implementation of a Working Vacation Policy

This paper introduces a double-orbit retrial queue model designed to address patient dissatisfaction by taking into account their willingness to pay for enhanced comfort and service. The system incorporates non-Markovian characteristics and employs a probability-generating function approach to solve its equations. Key performance metrics investigated include expected queue length, system length, and the precision of numerical results derived from empirical data. The model’s application is specifically examined within a hospital management system (HMS), underscoring its relevance in healthcare operations. Overall, the paper offers valuable insights into optimizing design strategies for retrial queue systems featuring unreliable servers, with a focus on enhancing patient satisfaction through personalized service offerings.