In Todays’ Scenario of Uncertain Business Environment and Fierce Competition, Organisations Don’T Leave any Stone Unturned to Stay Ahead of Others. They Often Introduce Lucrative Offers and Discounts to Attract Customers. These Encouraged Customers at Times Result Is Heavy Rush and Waiting Time of Customers at the Service Facility Increases. Long Waiting Time Results In Customer Impatience and Customers After Waiting For More Than Their Threshold Waiting Time Limit Abandon the Facility and Renege. Reneging Is a Loss to Business and It Is Very Important For an Organisation to Design Strategies In Advance to Retain the Reneging Customers. It Can Be Done Effectively If the Performance of the System Can Be Measured In Advance With some Probabilities. In This Paper a Single-Server Queuing Model Is Developed to Analyse the System Encountering Above Mentioned Challenges. the Model Is Then Solved Iteratively and Various Performance Measures Are Derived. Numerical Illustrations and Economic Analysis Are Presented. Sensitivity Analysis of the Model Is Also Performed to Study the Impact of Various Parameters on Cost Model Functions.