Using a device for close exponential networks of mass service a mathematical model for solving the problem of getting integral indexes of distributed information system on the basis of local computing network using file-server architecture was worked out. The heuristic algorithm of optimal placing the distributed data base onto local computing network knots according to the criterion of minimal average time of system reaction for users’ requests is represented. This algorithm uses the understanding of data bases as the points of multidimensional space and the knots in which those data bases are placed as clusters or classes. The results of numerical experiments are given.
Keywords: Distributed information system, distributed data base, local computing system, mass service network, conceptual model, exponential law of distributing the random value, stationary probability, mark process, the global balance equation, system reaction tim
Receiving adequate mathematical model requires studying of streams of inquiries into the information system which are described as random variables. The purpose of the analysis is definition of density function of distribution of random variables - time intervals between inquiries of users. The offered method contains stages at which check of independence and similarity of distribution of random variables is carried out, stationarities of a stream and the law of distribution of intervals of time between events is defined. For check of independence and similarity of distribution of random variables the criterias based on selective coefficients of correlation and the criteria which are based on the spectral density of intervals are used. For the analysis of stationarity of a stream of inquiries the standard methods of the smallest square regression and methods based on the analysis of special mathematical models are used. For example, Poisson's stream which parameter changes under some law is supposed. Sequences of the events displaced by casual influences are presented as the events happening according to the schedule with delays in the form of the independent and equally distributed random variables. For comparison of intensity of streams of inquiries from various users of information system the criterion based on the relation of function of maximum similarity and an index of dispersion is used. The offered technique is focused on using of the modern computer programs, for example, MatLab, Statistika.
Keywords: Modeling, inquiry, distribution, random variable, flow of events, intensity, statistical analysis, criterion, stationarity of the Poisson process, the level of significance
Using a device of close homogeneous exponential queueing networks (QN) a mathematical model of an information system functiouning with considering influence of blockings was worked out. A proccessor and the united resourse "channel - external memory" are considered as shared resources. All the users' requests are assumed to be single and homogeneous and the servicing discipline "First Come First Served" is used for sequence of their execution. Analytic expressions are given for calculation of the integral characteristics of the system: the distribuition law of number of messages in a system, the average number of messages at a node, the average sojourn time of a message at a node, the average sojourn time of a message in a system.
Keywords: Distributed information system, distributed data base, local computing system, mass service network, conceptual model, exponential law of distributing the random value, stationary probability, mark process, the global balance equation, system reaction tim