Research on the Queuing Theory based on M/M/1 Queuing Model

Abstract

A collection of mathematical theories and models make up queueing theory. The theory, which is derived from several models, makes an effort to recreate numerous typical queue waiting models. The purpose of this study is to do research on the M/M/1 queuing model-based queueing theory. After a brief introduction to the queuing theory, the independent indexes and the dependent variables will be shown. This paper contains some fundamental queuing theory formulas, some of which are specifically derived for the M/M/1 queuing model. This study then presents a simulation of the M/M/1 queuing model. Since some results are attained, this paper revealed some probability distributions and distribution functions of several indexes. The data characteristics displayed by these figures are very consistent with the daily life situation, which also proved the rationality and M/M/1 queuing model's applicability. By investigating this queuing theory, people shall be able to understand, analyze, and predict the phenomenon of waiting in a line.