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In this paper, we have developed a system for assigning customers to the routes based on their emotional state and age in Public Service Systems (PSSs). The Squeeze-and-Excitation (SE) method was used to develop the models, it improves the efficiency of the Deep Convolutional Neural Networks (DCNN) architecture by increasing the information flow between layers and enhancing important features. The method is based on compressing and exciting information at each convolution stage, which allows obtaining a vector of channel importance scores and using it to reweight the channels of the feature map. The study showed that this method allowed improving the quality of classification and reducing the model training time. The model of emotional target routing was developed based on the Newton interpolation polynomial to route customers based on their emotional state and age. The interpolation function in this model calculates the waiting time for customers according to their emotional state. Three models of binary classification of emotions and ages were developed, namely, two models for recognizing the emotional state of the customer, and one model for recognizing their age. The first and third models utilize DCNN from scratch using the new SE approach based on the attention mechanism. The second model uses the Support Vector Machine (SVM) method. The evaluate method was used to test the model after training, which allows evaluating the quality of the model on new data that was not used during training. This is done to check how accurately the model can predict the values of the target variable on new data. The evaluate method utilizes quality evaluation metrics such as accuracy, recall, and F1-score to assess the performance of the model. According to the experimental data obtained, the first and the second developed models achieved the validation accuracy of 72 % and 66 %, respectively, on the FER-2013 and Adience datasets. Their sizes were 0.69 MB and 369 MB, respectively. At the same time, the age recognition model achieved the accuracy of 88 % with the size of 1.68 MB. The mathematical model of emotional target routing (TERSS) was developed to minimize conflicts in public service systems. The developed system can automatically route customers based on their emotional state (presence of anger) and age to the appropriate operator. Thus, customers over 60 years old or with the anger level of 60–80 % are directed to a senior operator who knows how to communicate with elderly or emotionally excited customers, while customers with the anger level of 80–100 % are directed to a psychologist. This research can be applied in PSSs to detect the features of customers’ age and anger. Moreover, it can be applied in various areas where there is a contact with a large number of people, such as banks, supermarkets, airports access control systems, police stations, subways, and call centers.

The paper proposes a new solution for recognizing the emotional state of a person (joy, surprise, sadness, anger, disgust, fear, and neutral state) by facial expression. Along with traditional verbal communication, emotions play a significant role in determining true intentions during a communicative act in various areas. There is a large number of models and algorithms for recognizing human emotions by class and applying them to accompany a communicative act. The known models show a low accuracy in recognizing emotional states. To classify facial expressions, two classifiers were built and implemented in the Keras library (ResNet50, MobileNet) and a new architecture of a convolutional neural network classifier was proposed. The classifiers were trained on the FER 2013 dataset. Comparison of the results for the chosen classifiers showed that the proposed model has the best result in terms of validation accuracy (60.13 %) and size (15.49 MB), while the loss function is 0.079 for accuracy and 2.80 for validation. The research results can be used to recognize signs of stress and aggressive human behavior in public service systems and in areas characterized by the need to communicate with a large number of people.