Optimization Analysis of Ticket Queues with Balking Customers and Single Vacation Policy

Abstract

Self-checkout services have gained popularity across various industries, offering
Service systems issue numbered tickets for upon arrival customers without physical queues are popularly applied in public sectors. These systems are managed by ticketing technology and thus are different from those in common classical queues. This paper introduces a novel ticket queue that accounts for impatient customers and a single vacation policy. A schematic state-transition-rate diagram with the associated flow-balance equations is presented. The block-partitioned infinitesimal generator is provided in matrix form and the corresponding steady-state probabilities are solved recursively using the matrix-geometric method. We also derive explicit expressions of critical metrics relative to the performance measures. Numerical sensitivity analysis and graphical results are presented to assess the influence of various parameters on system characteristics. To reduce the computational complexity and enhance the analysis efficiency, we simplify the model and provide an efficient approximation method. Furthermore, a stepwise regression model is constructed to estimate the expected number of customers in the system without the need for complex matrix manipulations. Finally, applying the NSGA-II algorithm, a triple-objective optimization problem is investigated to determine the optimal operating condition with the minimum cost.