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.


March 12nd, 2019

15:30 ~ 16:30


Zhenghua Long, Hong Kong University


Room 102, School of Information Management & Engineering, Shanghai University of Finance & Economics