Performance Characteristics of Frame Slotted ALOHA Systems

• Main Authors: Kun-Shu, Huang, 黃崑書
• Other Authors: Chi-Kuang, Hwang
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/qg4h26

博士 === 中華大學 === 工程科學博士學位學程 === 107 === Framed slotted ALOHA (FSA) protocols have been widely used in diverse multiple access communication system. Consider an FSA system that consists of users and there are slots accommodated in a frame. Each user will randomly transmit a packet in one of the slots. Discrete probabilities for the event that there are exactly empty slots (no packet in the slot), , the event that there are exactly successful slots (one packet in the slot), , and the event that there are exactly collision slots (more than one packet in the slot), , have been formulated. Therein, based on the generic analytical approach (GAA) has been proposed, yet its numerical computation will become difficult when the number of slots is increasing. In this thesis, an exact closed-form formula (ECFF) for the probability of collision slots is derived. It can not only overcome the computational deficiency of GAA in the presence of a large numbers of slots, but also reduce the computation complexity of the collision probability. Surprisingly, a hybrid recursive equation can be formed by introducing a differentiation operator. Then after applying various algebraic properties of Laplace transform and Z transform, the final collision probability can be represented by a very compact double summation expression. The proposed ECFF and GAA have been verified by Monte Carlo simulation, and the computation time for both methods has been conducted, and the proposed ECFF is faster than that of GAA. In this thesis, we investigate further performance characteristics of FSA protocols. Specifically, we will develop mathematical expressions for the mean and variance of the events associated with the discrete probabilities. We believe that major contributions of this thesis can provide valuable information to characterize the behavior of various FSA based application systems.