Sensitivity of constrained Markov decision processes
Annals of Operations Research
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Critical Thresholds for Dynamic Routing in Queueing Networks
Queueing Systems: Theory and Applications
A Call-Routing Problem with Service-Level Constraints
Operations Research
Optimal Routing In Output-Queued Flexible Server Systems
Probability in the Engineering and Informational Sciences
The Slow Server Problem for Uninformed Customers
Queueing Systems: Theory and Applications
Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
On the incomplete results for the heterogeneous server problem
Queueing Systems: Theory and Applications
State space collapse in many-server diffusion limits of parallel server systems and applications
State space collapse in many-server diffusion limits of parallel server systems and applications
ACM SIGMETRICS Performance Evaluation Review
The Impact of Increased Employee Retention on Performance in a Customer Contact Center
Manufacturing & Service Operations Management
Control of a Heterogeneous Two-Server Exponential Queueing System
IEEE Transactions on Software Engineering
Quantifying fairness in queuing systems: Principles, approaches, and applicability
Probability in the Engineering and Informational Sciences
Service-Level Differentiation in Call Centers with Fully Flexible Servers
Management Science
Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems
Manufacturing & Service Operations Management
Queue-and-Idleness-Ratio Controls in Many-Server Service Systems
Mathematics of Operations Research
Admission control for a multi-server queue with abandonment
Queueing Systems: Theory and Applications
Dispatching to incentivize fast service in multi-server queues
ACM SIGMETRICS Performance Evaluation Review
On the Efficiency-Fairness Trade-off
Management Science
A Dispatching Model for Server-to-Customer Systems That Balances Efficiency and Equity
Manufacturing & Service Operations Management
Dynamic scheduling of a GI/GI/1+GI queue with multiple customer classes
Queueing Systems: Theory and Applications
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In a call center, there is a natural trade-off between minimizing customer wait time and fairly dividing the workload among agents of different skill levels. The relevant control is the routing policy, that is, the decision concerning which agent should handle an arriving call when more than one agent is available. We formulate an optimization problem for a call center with heterogeneous agent pools, in which each pool is distinguished by the speed at which agents in that pool handle calls. The objective is to minimize steady-state expected customer wait time subject to a “fairness” constraint on the workload division. We first solve the optimization problem by formulating it as a Markov decision process (MDP), and solving a related linear program. We note that this approach does not in general lead to an optimal policy that has a simple structure. Fortunately, the optimal policy does appear to have a simple structure as the system size grows large, in the Halfin-Whitt many-server heavy-traffic limit regime. Therefore, we solve the diffusion control problem that arises in this regime and interpret its solution as a policy for the original system. The resulting routing policy is a threshold policy that determines server pool priorities based on the total number of customers in the system. We prove that a continuous modification of our proposed threshold routing policy is asymptotically optimal in the Halfin-Whitt limit regime. We furthermore present simulation results to illustrate that our proposed threshold routing policy outperforms a common routing policy used in call centers (that routes to the agent that has been idle the longest).