This Is AuburnElectronic Theses and Dissertations

A Markov Chain Dynamic Social Network Modeling and Simulation to Assess the Impact of Out-of-School Suspensions on Dropouts and Truancy




Peters, Kim

Type of Degree



Industrial and Systems Engineering


Generally, a social network is mainly concerned with actors, the actions of actors, and the interactivities among actors in a community. Employing graph theory to represent overall social network structure, this study develops a Student School Attendance System (SSAS) evaluation model to provide a frame work in order to understand and assess the impacts of unsupervised Out-of-School (OOS) Suspensions on dropout, truancy, and the overall attendance performance of students and proposes a new attendance category, supervised out-of-school suspension. In recent years, there has been a dramatic increase in juvenile delinquency and student dropout rates. This research examines the impacts of a current OOS suspension program which is devoid of any form of supervision or monitoring system. In brief, the school transfers the problem student from the school to the street without any support mechanism. To examine and assess OOS, this research develops a model that represents current student attendance states paradigms considering student interaction by assimilating learning coefficients and threshold values for connectivity between peers. The study further examines student attendance for supervised versus unsupervised OOS. This research employs a Stochastic Markov Chain Process that considers the random events of the student school attendance phenomenon. The SSAS model represents a comprehensive state diagram of student school attendance categories based on graph theory and defines relevant parameters and variables. The model process begins with formulation of the initial transition probability and calculation of cumulative and steady state probabilities. The student school attendance states are determined based on random numbers and ranges of cumulative probability distributions applying the Markov Chain Memory-Less property. The next day student attendance probability computation considers the influence of friends by integrating a threshold value for dynamic connectivity and the fitness of the learning coefficient as the interaction influential factor among students. In addition, the SSAS model explores in three ways the development of the initial transition probability. The first model employs a pure random process by generating the initial transition probability of the student school attendance in a random selection scheme. The second model provides a controlling mechanism by providing the initial transition probability distribution for student school attendance via a pre-arranged input value data table. The third model provides a controlling mechanism as well as the stability in the system by implementing a pre-arranged output value look-up table which is formulated based on attendance data to generate the initial transition probability. Furthermore, the model also exploits the connectivity between the peers in three different ways: Median Connectivity, Virtual Connectivity, and Hybrid Connectivity. As a result of the SSAS model simulation, the Pre-Arranged Output Value model generated the most stable system among all three models with 1.4% error. In terms of connectivity, Virtual Connectivity produced the most connections between peers. In the SSAS model student school attendance assessment there was about 22% improvement in the number of students promoted to the next grade/graduated from high school under supervised OOS suspensions in comparison to unsupervised OOS suspensions. Among three types of connectivity, Virtual Connectivity produced the most improvement in the number of students succeeding at school. In conclusion, the SSAS model successfully rejects the null hypothesis “Implementation of Supervised Out-of-School Suspensions will have no effect on students’ attendance and graduation rate.”