Strategic Behavior and Social Welfare Optimization in a Batch-service Queueing System with Threshold Policy

This paper studies customers’ strategic behavior and social welfare in a batch-service queueing system with threshold policy. We focus on the selfish behavior of arriving customers and social welfare optimization under unobservable and observable cases. By incorporating startup and service costs, the impact of batch size and startup threshold on optimal social welfare is analyzed. The findings demonstrate that the threshold policy effectively reduces frequent startup and shutdown occurrences, thereby enhancing the system’s equilibrium social welfare. There is an optimal batch size and startup threshold that maximize social welfare in each case, although the optimal social welfare in unobservable cases is consistently lower than that in observable cases. Finally, using an actual batch-service queue with threshold policy for testing sudden infectious diseases as an example, the game between the government and the testing company is analyzed. Two types of games are considered: simultaneous decisions and sequential decisions. It is found that in the sequential decision game, the government should take the initiative to regulate the price to avoid causing an excessive financial burden.