Bayesian analysis of stay times in a system

The evaluation of traffic in a system is an important measurement in many studies. Counting the number of items in a system has applications in all processing operations. Electronic messages circulating in a network, clients shopping in a supermarket, students attending programs in a school, all are examples of entities entering, staying and exiting a system. In this article we introduce a Bayesian updating methodology for the gamma distribution of stay times in a system. The methodology was first developed for areas monitored by surveillance cameras. The number of people in the covered area was determined and the average stay time was estimated using a gamma probability distribution. We extend the application to the generic case and present a simple updating methodology for the estimation of the model parameters.