Three essays on the Bayesian analysis of discrete time queueing systems with applications on emergency room gridlocks

In this work, we develop a Bayesian framework for the analysis of discrete time queueing systems and their use in predicting emergency room gridlocks. In our first essay, we concentrate on the Bayesian analysis of a geometric discrete time queue with single and multiple servers. We bring inference methods for the system parameters as well as performance measures of the discrete time queues. We also release the assumption of stationarity in a system. In doing so, we construct a dependent structure between the arrival and service processes that creates ergodicity a priori. Finally, we provide a framework to handle the inference and analysis of systems with batch arrivals. The second essay relaxes the homogeneity assumption on the arrival and service rates of single server queues via a dependence structure based on Markov modulated environments allowing us to model random surges in the system characteristics. Additionally, we provide a method to perform inference on the number of states environment. An extension that creates dependent structures among the arrival and service rates of different classes, as well as the advantages of utilizing such a modification will also be presented. Finally, the third essay investigates the Bayesian analysis of discrete time queueing networks with an emphasis on the queueing network formed by the emergency room and the hospital. We develop a discrete time queueing network model on a Bayesian framework to approach this interaction. In doing so, we provide steady state characteristics of these networks as well as gridlocking probabilities conditioned on initial system status.