Enhancing queuing theory realism: analysis of reneging behavior impact on M/M/1 drive-thru service system

Individuals seeking services through drive-thru queuing and waiting, anticipate speedy service. However, long queues often prompt customers' impatience, leading to reneging and the early departure from a queue due to perceived excessive waiting. Reneging behavior is often disregarded in queuing analysis, undermining the accuracy and management of queues, resulting in a misrepresentation of real-world scenarios. This study delves into an extensive analysis of a 123-h M/M/1 drive-thru service queue, examining reneging probability and its correlation with customers’ sensitivity to arrival times. Findings reveal that the time between reneging events follows an Exponential distribution, challenging the assumption of a Poisson distribution for reneging rates. The traditional calculation of queue intensity neglects reneging and service abandonment, necessitating modifications to core queuing theory equations for practicality. Integrating reneging behavior enhances the theory’s applicability to real-life queuing dilemmas, improving accuracy and interpretability for effective queue management analysis and strategies, thus directly benefiting business management of queuing systems.