Queuing is a prevalent and vexing issue in various service systems, such as banks, restaurants, and supermarkets, where customers often endure prolonged wait times, resulting in discomfort and the potential loss of impatient patrons. Increasing service capacity might seem like a straightforward solution, but it invariably leads to escalated fixed and variable costs, making the optimization of this trade-off between revenue loss and cost a complex challenge for businesses. This study explores existing queuing models and proposes innovative approaches for addressing these critical issues