Collaborative Research: GOALI: Modeling and optimizing patient-flow dynamics in hospitals and hospital networks

One of the main drivers of complexity in a queueing system is the dependence between different random variables describing the system. For example, the queue lengths at different time points and the waiting times of different items (jobs, customers) in queue are dependent. To reduce dependence-related complexities, it is customary to assume that the system's primitives (such as the arrival processes, times spent in service, patience of different customers, etc.) are independent from one another. However, in many settings, dependencies between primitive processes and their corresponding random variables should clearly hold, in particular when service systems are considered. For example, it stands to reason that the service requirement of a customer depends on that customer's patience or on the time that customer spent waiting in queue. Indeed, recent empirical studies show that these types of dependencies exist in call centers and hospitals. A natural question to ask is: To what extent do these types of dependencies (referred to as "exogenous", to distinguish them from the "endogenous" dependencies that are induced via queueing effects), impact the performance and optimal design (e.g., staffing, control or pricing of services) of a service system? The proposed research aims to answer this question via a thorough study of systems with exogenous dependencies. It is significant that dependence between the primitives renders exact analysis intractable. Furthermore, the impacts of such dependence cannot be captured or ranked by a single parameter, such as Pearson's correlation coefficient, so that the entire joint distribution between the dependent primitives must be considered. Thus, various approximations, based on the entire joint distribution of the dependent primitives, are proposed, and the impact of the dependence is analyzed by employing stochastic dependence orders and copulas. Initial results demonstrate that the proposed approximations are accurate and ef