On processor sharing and its applications to cellular data network provisioning

To develop simple traffic engineering rules for the downlink of a cellular system using Proportional Fairness (PF) scheduling, we study the “strict” and “approximate” insensitivity of a Processor Sharing (PS) system, specifically for the Egalitarian (EPS) and Discriminatory (DPS) variants of PS. Assuming homogeneous channel conditions, all concurrent flows are allocated an equal share of downlink transmission slots regardless of flow types and locations. The cell system is modeled as an EPS queue. We prove the performance insensitivity of EPS in a relevant new case that has not been studied in the literature. Considering heterogenous channel conditions, the system is modeled as the DPS queue in which each traffic type is divided into subclasses with different assigned weights. Asymmetric weights among the subclasses model the unequal channel sharing that occurs with PF scheduling. Our results show that the first-order performance of the DPS is largely insensitive to the input traffic characteristics, as long as the weights among subclasses are not highly skewed. Our findings, confirmed by the simulation of a cellular system, imply reduced complexity for traffic provisioning procedures. However, our study also shows that the first-order performance is sensitive to the traffic details when there is discrimination among different traffic types. This observation implies that the introduction of differentiated services may pose a great challenge to network provisioning in future cellular systems.