In this study we applied queueing theory to analyze the problem of congestion in supermarket check-outs. We are particularly concerned with modeling the mean user waiting time in the queue, viewed as an important component of the user service, as a function of the capacity of the system (i.e., the number of cashiers in a given time period). Three models are explored: (i) to represent the system by means of a simple M/M/m queueing model, where m is the number of cashiers, (ii) to represent the system by means of m parallel and independent M/M/1 queueing models, and (iii) to represent the system by means of a more generic Markovian model, where the former models can be viewed as particular cases. In order to evaluate the performance of the models, we developed a case study in one of the supermarkets of Jaú-Serve chain located in São Paulo State. The results showed that the third model can yield a good approximation for the problem, different from the first two ones.
queueing theory; supermarkets; Markovian model
