On the optimality of a full-service policy for a queueing system with discounted costs
The paper considers a single-server queueing system in which the service rate is a dynamic decision variable. There is a server cost per unit time (a non-decreasing function of the service rate) and a holding cost per unit time (a non-decreasing function of the number of customers in the system). The objective is to minimize the expected discounted cost over a finite or infinite horizon. The paper begins with a semi-Markov decision model for a single-server queue with exponentially distributed inter-arrival and service times. Then it presents a general model with weak probabilistic assumptions and demonstrates that the full-service policy minimizes both finite-horizon and infinite-horizon total discount cost on each sample path.
scientific article; zbMATH DE number 5000146