Are the queueing systems in practice random or uncertain? Evidence from online car-hailing data in Beijing

In order to rationally characterize the nondeterministic phenomena in queueing systems, there exist two mathematical systems, one is probability theory concerned with the analysis of random phenomena and the other is uncertainty theory concerned with the analysis of uncertain phenomena. Before using the above two mathematical systems to model the real queueing systems, we often need to face such a question, are the real queueing systems random or uncertain? In order to answer this question, we collect the arriving times of passengers from online car-hailing platform in Beijing, and then analyze the collected data based on stochastic renewal process and uncertain renewal process. Finally, by comparing samples and confidence intervals of the total numbers of passengers arriving on the online car-hailing platform under two mathematical systems, we come to the conclusion that the queueing systems in the real world are uncertain rather than random.