How should rejection be used to maximize congestion while preserving idle time?

This study aims to identify a rejection policy that maximizes system congestion while maintaining a minimal proportion of idling time for agents. To achieve this, we focus on an M/M/s queue and leverage a Markov decision process to establish the threshold-based structure of the optimal policy. The optimal policy’s distinctiveness lies in rejecting all customers present when the threshold is attained. This policy’s determination holds significance, offering an upper boundary for the anticipated number of customers within a queueing system governed by a rejection policy. Furthermore, we present the performance metrics associated with the optimal rejection policy and offer asymptotic results that facilitate the computation of the optimal threshold.