Essays on Skills-Based Routing

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Service systems such as call centers and hospital inpatient wards typically feature multiple classes of customers and multiple types of servers. Not all customer-server pairs are compatible, and some types of servers may be more efficient at serving some classes of customers than others. In the queueing literature, the problem of matching customers and servers is known as skills-based routing. This thesis consists of two works I have done in this area. The first work, which is done jointly with Jing Dong and Pengyi Shi, considers the routing problem in the face of a demand surge such as a pandemic. It shows how future arrival rate information, which is often available through demand forecast models, can be used to route near-optimally, even when there may be prediction errors. The methods used involve fluid approximations and optimal control theory, and the policies obtained are intuitive and easy to implement. The second work, which is done jointly with Jing Dong, incorporates a staffing element in addition to routing. Asymptotically optimal staffing and scheduling policies are derived for an M-model, both with and without demand uncertainty. The methods used involve diffusion approximations and stochastic-fluid approximations.