A Diffusion Approximation for a Markovian Queue with Reneging
Queueing Systems: Theory and Applications
A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging
Queueing Systems: Theory and Applications
Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue
Queueing Systems: Theory and Applications
Optimal buffer size for a stochastic processing network in heavy traffic
Queueing Systems: Theory and Applications
Optimal control of parallel server systems with many servers in heavy traffic
Queueing Systems: Theory and Applications
Mathematics of Operations Research
Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations
Operations Research
Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems
Operations Research
The cμ/θ Rule for Many-Server Queues with Abandonment
Operations Research
Dynamic control of a single-server system with abandonments
Queueing Systems: Theory and Applications
On the asymptotic optimality of the cμ/θ rule under ergodic cost
Queueing Systems: Theory and Applications
Queues with Many Servers and Impatient Customers
Mathematics of Operations Research
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We consider a dynamic control problem for a GI/GI/1+GI queue with multiclass customers. The customer classes are distinguished by their interarrival time, service time, and abandonment time distributions. There is a cost c k 0 for every class k驴{1,2,驴,N} customer that abandons the queue before receiving service. The objective is to minimize average cost by dynamically choosing which customer class the server should next serve each time the server becomes available (and there are waiting customers from at least two classes).It is not possible to solve this control problem exactly, and so we formulate an approximating Brownian control problem. The Brownian control problem incorporates the entire abandonment distribution of each customer class. We solve the Brownian control problem under the assumption that the abandonment distribution for each customer class has an increasing failure rate. We then interpret the solution to the Brownian control problem as a control for the original dynamic scheduling problem. Finally, we perform a simulation study to demonstrate the effectiveness of our proposed control.