Relationship between guaranteed rate server and latency rate server

To analyze scheduling algorithms in high-speed packet switching networks, two models have been proposed and widely used in the literature, namely the guaranteed rate (GR) server model and the latency rate (LR) server mode. While a lot scheduling algorithms have been proved to belong to GR or LR or both, it is not clear what is the relationship between them. The purpose of this paper is to investigate this relationship. We prove that if a scheduling algorithm that belongs to GR, it also belongs to LR and vice versa. In addition, we review several other models that are also used for analysis of scheduling algorithms and discuss their relationship with LR model and GR model.