Healthcare systems are growing very fast, especially emergency departments (EDs) which constitute the major bottleneck of these complex concurrent systems. Emergency departments, where patients arrive without any prior notice, are considered real-time complex dynamic systems. Enhancing these systems requires tailored modeling techniques and a process optimization approach. A new mathematical approach is proposed in order to help multiple emergency units cooperate and share none-consumable resources to achieve the required flow. To achieve the cooperation, the process is modeled by a new subclass of Petri nets. The new Petri net model was proposed in a previous work and is used in this study in order to tackle the problem of modeling and managing these emergency units. The proposed Petri net is named Resource Preservation Net (RPN). Few theorems and lemmas are proposed to support the proposed Petri net model and to prove the correctness of cooperation and resource sharing. In this contribution, a model of cooperative healthcare units is proposed to achieve sound resource sharing and collaboration. The objective function of the proposed model is to improve the key performance indicators: patients length of stay (LoS), resource utilization rates, and patients waiting time. The cooperation among multiple EDs is then proposed through the study of merging two or more units. The cooperative and noncooperative behavior are also studied through theorems of soundness, separability and serializability, and a proof of scalability.
In this paper, a new process learning framework that is based on probabilistic learning and predicate logic is proposed. The input of this framework is a set of log files, and the output is a probabilistic predicate-based workflow that describes the process. This paper targets a methodology of learning processes given data and the learning algorithm finds out the logical operators that bind the events described in data and model it using predicate logic. While building the process, the probability of every event and the probabilities of the relationship between events are calculated. The learning process is an ongoing process, which means after learning when feeding the system with a new set of log files, the algorithm takes the previously learned process and it is set of probabilities as a starting state and starts modifying them based on the newly learned log files. This feature is very essential for those applications that integrate and interact with bigdata since for bigdata, starting the learning process from the beginning for every new set of data is not feasible. In this paper, the assumption is that log files are event-based, and every event is associated with its time of occurrence. Any event could have multiple occurrence times throughout the log files. The framework provides an optimal general definition of a process that is described by those log files. The process could change schematically or with respect to behavior when learning a new set of logs. In order to achieve what is described, a dependency matrix needs to be learned, and then the probability matrix is calculated. The outcome of the two matrices is a predicate-based workflow. Workflows can easily be described by Petri nets and Petri nets can map to predicate logic. The reason to convert the workflow into the knowledge base is the ability to infer new facts from given facts we conclude from log files. In this paper, we integrate a modification to α algorithm with the framework in order to describe dependencies and probability of occurrences of events. INDEX TERMS Big data, α algorithm, event logs, process mining, healthcare.
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