2019-03-12 | Zhenghua Long：Dynamic Scheduling of Multiclass Many-server Queues with Abandonment: the Generalized cμ/h Rule
We consider the problem of server scheduling in a multiclass many-server queueing system with abandonment. For the purpose of minimizing the long-run average queue length costs and abandon penalties, we propose three scheduling policies to cope with any general cost functions and general patience time distributions. First, we introduce the target-allocation policy, which assigns higher priority to customer classes with larger deviation from the desired allocation of the service capacity, and prove its optimality for any general queue length cost functions and patience time distributions. The Gcμ/h rule, which extends the well-known Gcμ rule by taking abandonment into account, is shown to be optimal for the case of convex queue length costs and nonincreasing hazard rates of patience. For the case of concave queue length costs but nondecreasing hazard rates of patience, it is optimal to apply a fixed priority policy, and a knapsack-like problem is developed to determine the optimal priority order efficiently. As a motivating example of the operations of emergency departments, a hybrid of the Gcμ/h rule and the fixed priority policy is suggested to reduce crowding and queue abandonment. Numerical experiments show that this hybrid policy performs satisfactorily.
Dr. Zhenghua Long is currently a Postdoc Scholar in the Department of Industrial Engineering and Decision Analytics at the Hong Kong University of Science and Technology under the supervision of Professor Jiheng Zhang. He was a research fellow in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He received his PhD degree in Operations Research from HKUST in 2015. Prior to that, he graduated from Department of Mathematics at Nanjing University in 2010. His research interests lie in asymptotic analysis and optimal control of queueing systems and their applications in manufacturing and services.