Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Call-Routing Schemes for Call-Center Outsourcing
Manufacturing & Service Operations Management
Optimal buffer size for a stochastic processing network in heavy traffic
Queueing Systems: Theory and Applications
Stochastic analysis of multiserver systems
ACM SIGMETRICS Performance Evaluation Review
Dynamic routing of customers with general delay costs in a multiserver queuing system
Probability in the Engineering and Informational Sciences
Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems
Manufacturing & Service Operations Management
On a Data-Driven Method for Staffing Large Call Centers
Operations Research
Control of systems with flexible multi-server pools: a shadow routing approach
Queueing Systems: Theory and Applications
Dynamic control of a single-server system with abandonments
Queueing Systems: Theory and Applications
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
Mathematics of Operations Research
Shadow-Routing Based Control of Flexible Multiserver Pools in Overload
Operations Research
Dynamic fluid-based scheduling in a multi-class abandonment queue
Performance Evaluation
Dynamic scheduling of a GI/GI/1+GI queue with multiple customer classes
Queueing Systems: Theory and Applications
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We consider a Markovian model of a multiclass queueing system in which a single large pool of servers attends to the various customer classes. Customers waiting to be served may abandon the queue, and there is a cost penalty associated with such abandonments. Service rates, abandonment rates, and abandonment penalties are generally different for the different classes. The problem studied is that of dynamically scheduling the various classes. We consider the Halfin-Whitt heavy traffic regime, where the total arrival rate and the number of servers both become large in such a way that the system's traffic intensity parameter approaches one. An approximating diffusion control problem is described and justified as a purely formal (that is, nonrigorous) heavy traffic limit. The Hamilton-Jacobi-Bellman equation associated with the limiting diffusion control problem is shown to have a smooth (classical) solution, and optimal controls are shown to have an extremal or "bang-bang" character. Several useful qualitative insights are derived from the mathematical analysis, including a "square-root rule" for sizing large systems and a sharp contrast between system behavior in the Halfin-Whitt regime versus that observed in the "conventional" heavy traffic regime. The latter phenomenon is illustrated by means of a numerical example having two customer classes.