Mathematical model of server requests intensity description

Abstract

The paper is devoted to the mathematical model development of non-stationary flow of requests from clients to the database in order to modulate the quality of service. The mathematical model of the queries number fluctuations to the database has the form of a regression equation and allows more accurate modeling of the connections pool size in the servlet. Connection pool is a pattern that helps to reduce responding time for queries to databases. To another hand the extra used memory wasting server resources. The task of calculating the optimal connection pool size could be solved by verity of mathematical apparatuses that demand information about intensity of stationary incoming queries flow. It is known, that real incoming queries flow is non-stationary. In the paper was suggested mathematical model of flow intensity fluctuations with daily and hourly harmonic vibrations. Statistics analyses of model adequacy was made, homogeneity of variances is checked, the significance of the coefficients of the regression equation was estimated. The obtained mathematical model describes fluctuations in the intensity of clients' requests to the servlet during the week. The mathematical model can be used to predict the load on the server or to build a simulation model of the query service system. The adequacy of the model is checked, the homogeneity of variances is checked, the significance of the coefficients of the regression equation is estimated, the adequacy of the regression equation is checked, the analysis of the autocorrelation of the residues is carried out. The results obtained in the article give further development for modeling process technologies in the field of information systems and can be used to calculate the load on the server with a non-stationary flow of requests from clients to the database.