On the principle of smooth fit for a class of singular stochastic control problems for diffusions
SIAM Journal on Control and Optimization
Diffusion approximation for GI/G/1 controlled queues
Queueing Systems: Theory and Applications
Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Dimensioning Large Call Centers
Operations Research
Heavy-Traffic Limits for the G/H2*/n/m Queue
Mathematics of Operations Research
A Bounded Variation Control Problem for Diffusion Processes
SIAM Journal on Control and Optimization
Optimal buffer size for a stochastic processing network in heavy traffic
Queueing Systems: Theory and Applications
A Numerical Method for Solving Singular Stochastic Control Problems
Operations Research
Asymptotically Optimal Admission Control of a Queue with Impatient Customers
Mathematics of Operations Research
Mathematics of Operations Research
Admission control for a multi-server queue with abandonment
Queueing Systems: Theory and Applications
Customer Abandonment in Many-Server Queues
Mathematics of Operations Research
Designing a call center with an IVR (Interactive Voice Response)
Queueing Systems: Theory and Applications
Refining Square-Root Safety Staffing by Expanding Erlang C
Operations Research
Queues with Many Servers and Impatient Customers
Mathematics of Operations Research
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We consider a controlled queueing system of the $$G/M/n/B+GI$$G/M/n/B+GI type, with many servers and impatient customers. The queue-capacity $$B$$B is the control process. Customers who arrive at a full queue are blocked and customers who wait too long in the queue abandon. We study the tradeoff between blocking and abandonment, with cost accumulated over a random, finite time-horizon, which yields a queueing control problem (QCP). In the many-server quality and efficiency-driven (QED) regime, we formulate and solve a diffusion control problem (DCP) that is associated with our QCP. The DCP solution is then used to construct asymptotically optimal controls (of the threshold type) for QCP. A natural motivation for our QCP is telephone call centers, hence the QED regime is natural as well. QCP then captures the tradeoff between busy signals and customer abandonment, and our solution specifies an asymptotically optimal number of trunk-lines.