Strategic admission in a finite-source queue with triadic control and working vacations

We study a finite-source, finite-capacity queueing game with triadic control, working vacations, and impatient customers. The model is formulated as a finite continuous-time Markov chain with level-dependent feasible phases under single and multiple working-vacation policies. Unlike infinite-source models, the finite-source structure requires a careful distinction between aggregate request opportunities in the complete system and the decision environment faced by a tagged customer. The exogenous balking mechanism of the underlying finite-source service model is replaced by a symmetric strategic joining probability. This allows us to characterize the individual equilibrium, define the socially optimal admission probability, and compare decentralized and socially optimal behavior. Numerical experiments indicate that the working-vacation policy is the main determinant of equilibrium behavior and welfare in the retained parameter regime, while impatience can locally affect the socially desirable admission level.