Theoretical Performance Analysis of Distributed Queue for Massive Machine Type Communications: Throughput, Latency, Energy Consumption

Massive machine type communications (mMTC) is one of main application cases in 5G, which is supposed to support communications of massive number of machine-type devices (MTDs). Distributed queue (DQ) is a variant of tree splitting protocol which combines an m-ary tree splitting algorithm with a set of simple smart rules, organizing every terminal in one out of two virtual queues. Theoretically, DQ allows access to infinite terminals and is stable under any traffic condition, which alleviates the unstable problem of slotted ALOHA, and is especially suitable for mMTC. However, its theoretical comprehensive performance analysis as well as related statistical characteristics is still missing, which severely restricts the full manifestation of its performance advantages. In view of this, the paper proposes a general performance analysis framework for DQ, with which full probability space of DQ evolution process is presented for the first time. To be more specific, probability distribution function (PDF), mean and variance of throughput, latency and energy consumption of DQ is analytically derived to comprehensively evaluate performance. Taking the IEEE 802.15.4 standard for mMTC as example, numerical results validate the accuracy of the proposed analysis framework and the stability of DQ, present effects of number of MTDs, number of contention slots ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> ), and maximum number of transmissions ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}$ </tex-math></inline-formula> ) on DQ in terms of aforementioned performance metrics. These results together provide good reference to find appropriate value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}$ </tex-math></inline-formula> to balance the performance metrics and enable more practical network optimization.