Modeling and analysis of telemental health systems with Petri nets

Abstract

Telemental health systems, a form of telemedicine, use electronic communication media to provide patients in remote locations access to psychological and psychiatric specialists. The structure of telemental health systems has a major impact on their performance. Discrete-event simulations offer useful results concerning capacities and utilization of specific resources. Simulation, however, cannot provide theoretical properties of analyzed systems. Petri net representations of systems can overcome this shortfall, offering a wide range of easily-analyzed and useful properties. Their ability to model resource conflict, parallel activities, and failure modes fits nicely with the reality of telemental health systems. Analysis of behavioral properties of Petri nets can provide meaningful information for system analysts. The most useful properties include net boundedness, liveness, and non-reachability of certain undesirable states. The thesis discusses methods to find all these properties. Specifically, it provides property-preserving net reductions to facilitate analysis of boundedness and liveness and describes an integer programming model to solve reachability and coverability problems. Moreover, this thesis outlines a simulation analysis of synchronous and asynchronous telemental health systems. The paper then describes a Petri net model of a generic telemental health delivery system. The paper subjects the model to an integer programming model and net reduction. The integer programming model indicated that the number of resources in the system remains static, full utilization of resources at a given time is possible, conflict over resources is possible, and improper work prioritization is possible within the model. Net reduction and analysis with open-source software showed that the model is bounded and live. These results can aid telemedicine system architects in diagnosing potential process issues. Additionally, the methods described in the paper provide an excellent tool for further, more granular analysis of telemedicine systems.