Analysis of Statistical Characteristics of User Arrival Process to the Testing Service

As a part of e-Learning system the testing service allows to measure students' skills. In order to design testing service it is necessary to study interaction between a student as the user of service and the testing service. We measure and analyze the time between requests and the testing service. By using KS-method we fit the measurement results to the theoretical probability distribution. The conducted analysis shows that the use of a normal model for analyzed data is not suitable. It is found that the inter-request time distribution is the log-logistic distribution. The estimates of the distribution parameters will be suitable for all such interactions between the user and the testing service. The homogeneity hypothesis for inter-request times is verified. The nonparametric Kruskal-Wallis test is applied as a homogeneity test. Then in order to aggregate observations into larger groups the cluster analysis of the log-logistic distribution parameters is carried out. The following methods of the cluster analysis are used: an agglomerative hierarchical clustering method and a k-means method. The results of our study can be used for the modeling of computer-based testing service.