Capacity Allocation and Scheduling in Two-Stage Service Systems with Multi-Class Customers

This paper considers a tandem queueing system, in which stage 1 has one station serving multiple classes of arriving customers differing in their service requirements and related delay costs, and stage 2 has multiple parallel stations, each of which provides one type of service. Each station has many statistically identical servers. The objective is to design a joint capacity allocation between the stages/stations and scheduling rule of different classes of customers to minimize the long-run average cost.Using fluid approximation, we convert the stochastic problem into a fluid optimization problem and develop a procedure to solve it. Based on the solution to the fluid optimization problem, we propose a simple and easy-to-implement capacity allocation and scheduling policy, and establish its asymptotic optimality for the stochastic system. The policy has explicit index-based forms for two special system structures: the many-to-one and one-to-many systems. We further propose a grouping and pooling strategy to streamline the operations of the service system. Finally, we conduct numerical experiments to validate the accuracy of the fluid approximation, and quantify the effect of grouping and pooling based on fluid optimal solution.Tandem queueing systems are ubiquitous. Our results provide guidelines on the allocation of limitedresource and scheduling of customer service in those systems. Our proposed policy would improve the system’s operational efficiency and customers’ service quality