Queueing model analysis of shopping malls in COVID-19 pandemic era: a case study

Queueing forms a daily routine of our lives wherever there are limitations in resources with competition. The ongoing Coronavirus Disease of 2019 (COVID-19) pandemic undeniably has its impacts on people's daily life. That in turn affected the number of customers who used to go outside for different outdoor activities. In this paper, a shopping mall is considered as a case study to propose an appropriate queueing model within these current pandemic circumstances. The proposed model consists of an open network with 10 nodes represent different real-existing serving stations. The queueing model is first analysed to check its stability that is evident analytically on the long run. The performance of the proposed network model is investigated using different measures. Based on recorded arrival and service rates, the mathematical derivations show that the traffic intensity of the system is still below 1, hence ensures stability. Also, the average number of customers in the network is 16.76 customers with only 2.66 customers awaiting in queues. Furthermore, the mean time a customer spends in the queue is only 0.16 min from a total spend on the network about 1.006 min. This indicates that the majority of time customers spend is in service with a very short waiting time due to current COVID-19 pandemic consequences, and the waiting time and queue lengths will undoubtedly increase once normal social life resumes.