Asymptotically optimal control of N-systems with H~*_2 service times under many-server heavy traffic

摘要

We address a control problem for a queueing system, known as the 'N-system," under the Halfin-Whitt heavy-traffic regime. It has two customer classes and two server pools: servers from one pool can serve both customer classes, while servers from the other pool can only serve one class. The service time is assumed to follow a special case of hyper-exponential distributions, called the distribution, and customers are impatient. We consider an expected infinite-horizon discounted cost function, with linear holding and abandonment cost components. A static priority policy is proposed and is shown to be asymptotically optimal in a certain parameter regime, using weak convergence techniques.