# User Utility Maximization in Narrowband Internet of Things for Prioritized Healthcare Applications
## 4 Design of the PAUM System
### Event Influenced Prioritized Data Transmission Access Scheduling  
In the proposed PAUM system, algorithms and optimization functions are executed in the eNBs. After determining event types, an eNB sends specific transmission slots to the UEs according to their event priorities so as to achieve maximum utility. Individual data sources follow the eNB for sending sensory data. In this section, we formulate two consecutive algorithms intended for an event-influenced priority scheduling to be executed in the eNBs. The Algorithm 1 generates a probabilistic event recognition output for a single channel based on gathered vital signs in a specific time window. A vital sign is defined as a sign that aids in the detection or monitoring of medical disorders or the measuring of a live organism's physiological function [30]. Vital signs are proof of the body's current physical functioning, providing important information such as blood pressure, pulse rate, breathing rate, etc., to determine the urgency. The Bayes Theorem [29], which is based on hypothesis and associated individual training data, was used to determine the most likely event type (Critical, Relevant, or Normal). In this algorithm, \(N\) is the set of UEs, \(V\) is the set of vital signs, and \(S\) is the set of hypotheses used as input. In lines 1-11, the vital sign readings and their thresholds are exploited to categorize traffic types--critical training data \(\partial_{C}\), relevant training data \(\partial_{R}\), and ordinary training data \(\partial_{N}\), having priorities 1, 2, and 3, respectively, where the lower number represents higher priority. Note that the relevant training data are revealed by combining two propositions--\(C_{v}\): \(V_{n}^{C}\) is a critical vital sign; and \(R_{v}\): \(V_{n}\) is a supporting vital sign for any critical event,The implication \(C_{v}\to R_{v}\) denotes whether a critical event needs the support of another vital sign. If the supporting vital sign is required for the associated critical event of that particular moment, it is counted as relevant training data. It then employs Bayesian learning to determine the probability of an occurrence based on new data that is connected to the event in lines 12 to 13. In fact, Bayesian approaches can incorporate probabilistic prediction hypotheses. In PAUM, the hypothesis is a vector of six constraints, specifying the values of the six attributes of vital sign, location(cabin, OPD, Emergency, Remote), range, forecast, decision, and type, and combines training examples for the target concept \"Event type\". Finally, the algorithm searches the maximally probable hypothesis by MAP (Maximum a posteriori) hypothesis, which returns the most probable event determination in lines 14 to 17. Then, Algorithm 1's outputs are received by Algorithm 2 as \(s_{n}\)--the sorted probabilistic determination of events. Another input is \(d_{n}\), the UEs' delay deadline for individual positioned events. Initially, the priority value is inserted in \(P_{n}\) applying the \(n^{th}\) positioned UEs vital sign record using function PRIORITY(\(V_{n}\)) on line 2, and that UE is placed in a subsequent Queue position. Then, in lines 3-4, the priorities and queue positions are updated depending on the delay deadline values of two consecutive events given that they have a very small difference (\(\epsilon\)) in their \(\delta\) values. It assists us in assuring that important packets are transmitted earlier than others. Finally, sorted priority events are stored in a queue as a result of Algorithm 2. ```
0:\(\hat{s}_{n}\gets s_{n}\) sorted in descending order.