Optimality of routing and servicing in dependent parallel processing systems
Queueing Systems: Theory and Applications
Mathematics of Operations Research
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SIGMETRICS '97 Proceedings of the 1997 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
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Mathematics of Operations Research
Optimal Control: Basics and Beyond
Optimal Control: Basics and Beyond
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Designing a Call Center with Impatient Customers
Manufacturing & Service Operations Management
RTSS '96 Proceedings of the 17th IEEE Real-Time Systems Symposium
Real-time queueing network theory
RTSS '97 Proceedings of the 18th IEEE Real-Time Systems Symposium
A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging
Queueing Systems: Theory and Applications
Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Dynamic routing of customers with general delay costs in a multiserver queuing system
Probability in the Engineering and Informational Sciences
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Queueing Systems: Theory and Applications
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We propose a general Markovian model for the optimal control of admissions and subsequent routing of customers for service provided by a collection of heterogeneous stations. Queue-length information is available to inform all decisions. Admitted customers will abandon the system if required to wait too long for service. The optimisation goal is the maximisation of reward rate earned from service completions, net of the penalties paid whenever admission is denied, and the costs incurred upon every customer loss through impatience. We show that the system is indexable under mild conditions on model parameters and give an explicit construction of an index policy for admission control and routing founded on a proposal of Whittle for restless bandits. We are able to gain insights regarding the strength of performance of the index policy from the nature of solutions to the Lagrangian relaxation used to develop the indices. These insights are strengthened by the development of performance bounds. Although we are able to assert the optimality of the index heuristic in a range of asymptotic regimes, the performance bounds are also able to identify instances where its performance is relatively weak. Numerical studies are used to illustrate and support the theoretical analyses.