RENEGING BEHAVIOR ON DRIVE-THRU QUEUES: A CASE STUDY-BASED APPLIED MATHEMATICAL INVESTIGATION
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Date
2023-03-02
Authors
Ayman Wasef Mohammad Dbeis
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Abstract
Drive-thru service was never exclusive for fast food restaurants only, but it is still more common for them. During the COVID-19 pandemic, drive-thru services extended to the health sector as well, to maintain the physical distancing. Palestine barely includes fully-active integrated drive-thru services; however, an expansion for full infrastructure drive-thru services is expected in the near future.
Whenever there is a need to obtain the service by queuing and waiting, queued customers show prominently their desire to be served as fast as possible. Impatient customers’ behaviors appear clearly in two main acts: reneging and balking. Reneging, as the main scope of this study, is one of ignored behaviors in queuing analysis, which makes analyzing and managing queues not reflecting the reality of queuing. This is due to the limited knowledge about such an event and factors leading to its occurrence.
This research aims to reach a deeper understanding of the queuing theory and the queue’s characteristics, to make it more reflective and interpretive to real life queuing problems. This is done by analyzing the behavior of impatient reneging customers, and identifying how their decision is affected by the queue’s characteristics.
Through non-participant observations, the required data were manually collected using surveillance camera recordings for Rio Café’s drive-thru service in Al-Bireh City. Given the purpose of this study, the data were mathematically analyzed to determine the probability distribution functions of the reneging behavior and the factors affecting waiting customers’ decision. In addition, linear and non-linear regression models were developed to predict the reneging rate and the relative frequency of reneging customers.
The study showed that the exponential distribution is the probability distribution function of the time intervals between successive reneging events of at least one reneging customer per time interval. However, the reneging rate does not follow the Poisson distribution.
It was concluded that the long waiting time is not the only factor causing impatient customers to renege on the queue, but other important factors affect this behavior. These factors are integrated and jointly distributed, leading to the customer's decision to leave the queue.
Keywords: Reneging Behavior, Impatient Customers, Retention, Queuing Theory, Joint Probability Distribution, Spatial-Dynamic Modelling.