Dynamic Optimal Control of Retrial Queueing Systems with Multiple Customer Classes

Motivated by call center systems, we investigate the optimal admission control problem for a retrial queueing system with multiple customer classes. Arrivals follow independent Poisson processes, service times are exponentially distributed, and the decision maker possesses complete information on the system state. The problem is formulated as a discrete-time Markov decision process via uniformization, with the objective of maximizing the long-run average profit. We analyze the structural properties of the optimality equation and the corresponding value functions. It is shown that the optimal policy is necessarily of threshold type. Moreover, we establish the monotonicity of the optimal threshold with respect to the system parameters, including arrival rates, service rates, and retrial intensity. Based on these theoretical characterizations, we develop a modified value iteration algorithm that exploits the threshold structure to reduce computational complexity. Numerical experiments demonstrate that the proposed algorithm achieves a reduction in computation time by a factor of approximately four compared with the classical value iteration scheme.