Bit-Level Power-Law Queueing Theory with Applications in LTE Networks

Though the classical packet-level queueing theory, which treats each packet as an entry, has achieved a great success in network analysis, it can be inaccurate when directly applied to long-term evolution (LTE) networks. This is because arriving packets could be broken down at the LTE base station server across adjacent transmission time intervals (TTIs), which are the smallest scheduling time units in LTE networks. In this paper, we first propose an innovative bit-level queueing theory to address the challenges in performance analysis of LTE networks. To consider the randomness in packet arrivals and packet lengths, we propose two representative compound network traffic models-Poisson-Exponential (PE) and Zeta-Pareto (ZP) models-to approximate light-tailed and heavy-tailed network traffic, respectively. PE models are suitable for conventional voice and low-speed services, while ZP models, which compound power-law distributions, describe complicated high-speed network applications. We derive tail asymptotics for the distributions of the number of bit arrivals in one TTI and the corresponding waiting time. Based on the results in bit-level queueing theory, we present engineering applications that take into account user experience, including estimating the user experience rate (UER), the busy UER and hourly traffic volume. The theoretical results are then validated through extensive simulations. Our novel traffic estimation approach has been adopted by Wireless Product Line at Huawei for network capacity planning and also projected to International Telecommunication Union (ITU) to compose 5G standards.