Essays on capacity sizing and dynamic control of large scale service systems

In this dissertation we solve two queueing control problems that are related to capacity sizing and dynamic outsourcing in call centers. First we take the capacity (staffing) decision as given and focus on the dynamic control (outsourcing) problem by solving an admission control problem for a multi-server queue with abandonment. We establish that a threshold policy is optimal through Markov Decision Process (MDP) analysis and present an algorithm to derive the optimal threshold that minimizes the long-run average cost. We also solve the approximating diffusion control problem (DCP) that arises in the Halfin-Whitt many-server limit regime. We show that the optimal policy is again of threshold form and that the parameter space has a sharper division in the sense that there is an optimal solution with a finite threshold level when the cost of an abandonment exceeds the cost of rejecting a customer; otherwise, there is an optimal solution that exercises no control. Furthermore, we devise an asymptotically optimal control policy based on the DCP solution and show that the proposed policy works extremely well even for small number of servers. Finally, we incorporate the upfront staffing decision that must made with partial knowledge of the arrival rate distribution and derive asymptotically optimal staffing policies.