Delays are a pervasive challenge in various real-world systems, including transportation, communication, and production. This research aims to analyze these delays and explore mathematical methods to model and mitigate their effects. Using real-world examples such as traffic congestion, network latency and production bottlenecks, it becomes clear that delays are ubiquitous and that effective management strategies are required. In our study, queueing theory, differential equations and optimization techniques are used to investigate different delay scenarios. Queueing theory is used to model and predict queues, e.g. with the M/M/1 queueing model, while differential equations, in particular delay differential equations (DDE), describe the dynamics of systems with inherent delays. Optimization techniques, including linear programming, provide solutions to minimize waiting times and improve efficiency under given constraints. Case studies on controlling traffic flow, reducing latency in networks, and optimizing manufacturing processes demonstrate the practical applications of these mathematical methods. For example, optimizing the timing of traffic signals using queueing theory leads to a significant reduction in urban traffic delays, while improved routing protocols reduce network latency. In manufacturing, DDE is used to optimize production schedules to increase overall efficiency. Our results indicate significant performance improvements in these systems, demonstrating the effectiveness of mathematical modeling and optimization. The study concludes that while delays are an inherent part of various systems, strategic mathematical approaches can significantly mitigate their effects. Future research will focus on advanced mathematical techniques and the integration of real-time data to achieve further improvements.