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

Abstract

Recently, increased measures are being devised to reduce crowdedness as a countermeasure for the spread of COVID-19. In this study, we propose a solution to reduce intra-facility crowdedness based on the usage of Wifi networks. This study maximizes the Wi-Fi logs that are continually generated in vast quantities in the ever-expanding Wi-Fi network environment to calculate the transition probabilities between nodes and the mean stay time at each node. Then, we model this data as a continuous-time Markov chain to obtain the variance of the stationary distribution, which we use as a metric of intra-facility crowdedness. Therefore, to minimize intra-facility crowdedness, we solved the optimization problem using stay rate as a parameter and demonstrated a numerical solution. In the optimization results, we succeeded in reducing intra-facility crowding by approximately 30%. This solution is a realistic approach for reducing intra-facility crowdedness as it makes adjustments to people’s stay times without any changes in their movements. We used the k-means method to categorize Wi-Fi users into a set of classes and documented the behavioral characteristics of each class, which helped implement class-specific measures to reduce intra-facility crowdedness. This enables facility managers to implement fine-grained countermeasures against crowdedness according to circumstances. Herein, we describe our computing environment and workflow for the basic analysis of vast quantities of Wi-Fi logs. Because the data we used are general-purpose, we believe that this research will be useful for both analysts and facility operators.