On the Effect of the Time Step in Discrete-Time Framework Analysis

In classic communication systems, signals and data were mostly continuous in time, such as voice (fixed and mobile telephony, and radio systems) and video signals (Television services), Conversely, in modern communication systems, most signals are packet-based (text and images in messaging services and social media) and even continuous-time data has to be converted into a discrete-time nature data, such as video and voice services that are now discretized to be sent in packet-based communication systems. However, these classic communication systems were analyzed, studied, and designed using continuous-time analysis, such as the classic Erlang-B formula. This classic analysis can still be used in modern systems, but a discrete-based framework provides a seamless analysis and yields more accurate results. In this work, the effect of the system’s elementary time step is analyzed, and guidelines for its selection are provided to adequately analyze continuous-time systems within a discrete-time framework. To demonstrate the utility of the discretization and to consider these guidelines, we developed a mathematical analysis based on a discrete-time Markov chain to study a system with a buffer capacity under conventional and bursty traffic, which is commonly found in an Internet of Things application. The derived formulas allow us to quantify system performance under a discrete framework. This, in turn, allows us to provide some relevant guidelines for the elementary time step selection to adequately analyze continuous-time systems under a discrete-time framework.