Martingale Theory Application to the Delay Analysis of a Multi-Hop Aloha NOMA Scheme in Edge Computing Systems

Abstract

This paper analyzes the end-to-end delay performance in an edge-computing scenario where a set of Internet of Things devices (IoTDs) access the computation facilities of an Edge Node by means of a 5G based network. In particular, the paper deals with a two power levels slotted Aloha non-orthogonal-multiple-access (NOMA) scheme and formulates a stochastic end-to-end delay bound, in terms of complementary cumulative probability distribution, by resorting to the application of the martingale theory. In order to validate the proposed analysis, the paper proposes comparisons between the achieved analytical predictions and actual values derived by resorting to extensive computer simulations. Furthermore, the well known Boole bound has been formulated and compared with the proposed Martingale approach to highlight the better behavior of the proposed solution.