Virtual allocation policies for many-server queues with abandonment

Zhenghua Long () and Jiheng Zhang ()
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Zhenghua Long: Nanjing University
Jiheng Zhang: Nanjing University

Mathematical Methods of Operations Research, 2019, vol. 90, issue 3, No 4, 399-451

Abstract: Abstract We study a multiclass many-server queueing system with renewal arrivals and generally distributed service and patience times under a nonpreemptive allocation policy. The status of the system is described by a pair of measure-valued processes to track the residual service and patience times of customers in each class. We establish fluid approximations and study the long-term behavior of the fluid model. The equilibrium state of the fluid model leads to a nonlinear program, which enables us to identify a lower bound for the long-run expected total holding and abandonment costs and design an allocation policy to achieve this lower bound. The optimality of the proposed policy is also demonstrated via numerical experiments.

Keywords: Multiclass queue; Customer abandonment; Fluid limits; Measure-valued processes (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00186-019-00683-9

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