Model reduction aims to decrease this computational strain by producing significantly smaller models that are faster and less expensive to simulate than the original large-scale systems which play a vital role in the complex physical phenomena. The goal of this paper is to gather information from different existing research works and summarize the current advancements in managing index-2 discrete-time (DT) descriptor-systems. In this paper, we look at three different methods for dealing with DT systems and compare them based on how well they work and how accurate they are. We also study the iterative approaches for the approximate solutions of the Smith method and the Alternating Direction Implicit (ADI) methods are used in different ways to make the Balanced Truncation (BT) method more effective. The iterative rational Krylov algorithm (IRKA) is used to approximate the original model by moment-matching. A comparative analysis of the different Model Reduction Methods (MOR) algorithms is illustrated to recognize the pros and cons of different approaches and the appropriate use of different MOR strategies.