Learning to Admit Optimally in an $M/M/k/k+N$ Queueing System with Unknown Service Rate

Understand

Motivated by applications of the Erlang-B blocking model and the extended $M/M/k/k+N$ model that allows for some queueing, beyond communication networks to sizing and pricing in production, messaging, and app-based parking systems, we study admission control for such systems with unknown service rate.

• In our model, a dispatcher either admits every arrival into the system (when there is room) or blocks it.
• Every served job yields a fixed reward but incurs a per unit time holding cost which includes the waiting time in the queue to get service if there is any.
• We aim to design a dispatching policy that maximizes the long-term average reward by observing arrival times and system state at arrivals, a realistic decision-event driven sampling of such systems.