Optimizing intra-facility crowding in Wi-Fi environments using continuous-time Markov chains

Various measures have been devised to reduce crowdedness and alleviate the transmission of COVID-19. In this study, we propose a method for reducing intra-facility crowdedness based on the usage of Wi-Fi networks. We analyze Wi-Fi logs generated continually in vast quantities in the ever-expanding wireless network environment to calculate the transition probabilities between the nodes and the mean stay time at each node. Subsequently, we model this data as a continuous-time Markov chain to determine the variance of the stationary distribution, which is used as a metric of intra-facility crowdedness. Therefore, we solved the optimization problem by using stay rate as a parameter and developed a numerical solution to minimize the intra-facility crowdedness. The optimization results demonstrate that the intra-facility crowding is reduced by approximately 30%. This solution can practically reduce intra-facility crowdedness as it adjusts people’s stay times without making any changes to their movements. We categorized Wi-Fi users into a set of classes using the k-means method and documented the behavioral characteristics of each class to help implement class-specific measures to reduce intra-facility crowdedness, thus enabling facility managers to implement effective countermeasures against crowdedness based on the circumstances. We present a detailed description of our computing environment and workflow used for the basic analysis of vast quantities of Wi-Fi logs. We believe this research will be useful for analysts and facility operators because we have used general-purpose data for analysis.