In this thesis, we present two key metrics for measuring the freshness of information in queueing systems: latency and age of information. We begin with an overview of fundamental concepts in probability theory, which form the basis for further discussion. We introduce some of the most important distributions, their properties, and the relationships between them. We continue with an introduction to the basics of queueing theory, a specific subfield of probability theory. In the following chapter, we focus on the metrics of age of information and latency within the context of queueing theory. We explain the differences between them, present their values in certain models, and discuss variations of the metric age of information, such as peak age of information. We approach the problem of calculating the values of these metrics in two ways: analytically and numerically. For the numerical approach, we use the Python programming language.
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