The study investigates the dynamics of heterogeneous multiserver queueing systems, where servers operate at different service rates-a scenario often encountered in practice but not captured by classical models. In traditional models, servers are assumed to be homogeneous, serving customers at the same rate, and customers are expected to select servers at random when multiple options are available. However, these assumptions often fail in real-world systems. This research develops a mathematical framework to model and analyze queues where servers have different service speeds. In such systems, a customer at the head of the queue may strategically choose to wait for a faster server, even when slower servers are idle, effectively blocking the queue. This decision-making behavior can improve system efficiency and preserve the "first-come, first-served" principle. However, customers may lose patience over time and opt to be served by the slow server, adding further complexity to the system. In this article, a two-server model that incorporates server preferences and customer hesitation is proposed, and Kolmogorov's forward equations for the corresponding transition probability functions are derived. Simulation experiments are used to illustrate behaviour of the system under various parameter settings. The impact of server heterogeneity and customer decision-making on overall system efficiency is explored.