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Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain,

t informed and intelligent decisions can be made in their management. Then, the mathematical analysis of the models would yield formulas that presumably relate the physical and stochastic parameters to certain performance measures, such as average response/ waiting time, server utilization, throughput, probability of buffer overflow, distribution function of response/waiting time, busy period of server, etc. The art of applied queueing theory is to construct a model that is simple enough so that it yields to mathematical analysis, yet contains sufficient detail so that its performance measures reflect the behavior of the real system. In the course of modeling one could use analytical, numerical, asymptotic, and simulation methods integrated into performance evaluation tools. In the course of modeling we make several assumptions regarding the basic elements of the model. Naturally, there should be a mechanism by which these assumptions could be verified. Starting with testing the goodness of fit for the arrival and service distributions, one would need to estimate the parameters of the model and/or test hypotheses concerning the parameters or behavior of the system. Other important questions where statistical procedures play a part are in the determination of the inherent dependencies among elements and dependence of the system on time.