Scheduling to Differentiate Service in a Multiclass Service System

Dynamic Scheduling to Differentiate Delay-Based Service Levels in Multiclass Service Systems Tail probability of delay (TPoD), defined as the probability that the customer delay exceeds a customary delay target, is widely used as a performance metric in many real-world service systems. Examples include the 80–20 rule in customer contact centers and the Canadian triage and acuity scale (CTAS) guideline that classifies patients in the emergency department into five acuity levels. In those settings, how to ensure that diverse customer needs are met based on prescribed TPoD targets via effective capacity planning and dynamic resource allocation has been deemed notoriously difficult. In response to such a challenge, in “Scheduling to Differentiate Service in a Multiclass Service System,” Yunan Liu, Xu Sun, and Kyle Hovey study a practical queueing system having multiple customer classes, nonstationary customer arrivals, and customer abandonment. They devise a new class of staffing (number of servers) and scheduling (assigning newly idle servers to a waiting customer from one of the classes) policies that can help achieve class-differentiated service levels measured by TPoD. This newly proposed class of control rules not only exhibits nice separation of scales under appropriate heavy-traffic scaling, but also gives rise to novel heavy-traffic stochastic-process limits for delay-related performance measures. The effectiveness of their approach is substantiated by heavy-traffic asymptotic stability theorems and extensive numerical studies in which important managerial insights are also generated. Motivated by large-scale service systems, we study a multiclass queueing system having class-dependent service rates and heterogeneous abandonment distributions. Our objective is to devise proper staffing and scheduling schemes to achieve differentiated services for each class. Formally, for a class-specific delay target w i > 0 and threshold α i ∈ ( 0,1 ) , we concurrently determine an appropriate staffing level (number of servers) and a server-assignment rule (assigning newly idle servers to a waiting customer from one of the classes), under which the percentage of class- i customers waiting more than w i does not exceed α i . We tackle the problem under the efficiency-driven many-server heavy-traffic limiting regime, where both the demand volume and the number of servers grow proportionally to infinity. Our main findings are as follows: (a) class-level service differen