Implementation of automated independent replications in the simulation of queuing systems

Abstract

This paper presents a basic idea of the method entitled 'Automated Independent Replications with Gathering Statistics of Stochastic Processes'. The mathematical foundation of the method is offered, as well as some recommendations for practical implementation of the met hod in the form of a computer program algorithm. A set of different expert knowledge needed for a successful development of conceptual and simulation models is pointed out in a separate review. The method has been tested in the modeling and simulation of queuing systems. Multidisciplinary character of simulation modeling This paper presents a basic idea of the method entitled 'Automated Independent Replications with Gathering Statistics of Stochastic Processes'. A clear review of expert knowledge needed for successful development of a conceptual model as well as a simulation one is offered. Simulation modeling of systems and processes in any military branch assumes a multidisciplinary approach. This is not a consequence of a free choice, but of needs and problems which arise in a research process and which require synchronized use of knowledge from different areas and scientific disciplines. In studies of queuing systems, these disciplines are: queuing theory, probability theory, mathematical statistics, stochastic processes, mathematical analyses, Monte Carlo simulation modeling, computer programming, knowledge about a real system under study, etc. Specific features of real queuing systems Consistency, fidelity or agreement of the model with the real system under study is one of the most important characteristics of the model. This means that a conceptual model should present reality as it really is. In the context of queuing system modeling, this means the following: if a real system works for some finite time, then the same should be applied for a model as well; if there can be any traffic intensity including overloading, then a model should be conceived accordingly, etc. Mathematical basis of the AIRGSSP method The mathematical basis of the method is offered, as well as some recommendations for practical implementation of the method in a form of a computer program algorithm. Explicitly, the mathematical foundations of the AIRGSSP method are three statements; the first one, the Bernoulli law of large numbers, or the first limit theorem: the frequency of one random event in a many times repeated experiment tends to the probability of that event; the second one, the perception of the behavior of a queuing system as a kind of a stochastic process, and the support for the statistics of stochastic processes; and the third one, the use of an interval estimation of proportion for establishing the control of the simulation result accuracy. Description of the implementation of the AIRGSSP method The application of the AIRGSSP method includes the following: development of a conceptual model; definition of performance measures; development of the basic structure of the simulation model; implementation of a module for the stochastic process statistics; implementation of a module for automatization of independent replications of the simulation experiment; calculation of a number of replications of the simulation experiment; and translation of the model into the computer code. Conclusion A detailed description for the practical implementation of the method 'Automated Independent Replications with Gathering Statistics of Stochastic Processes' is given. The capacity and advantages of the AIRGSSP method are particularly clear in the cases of modeling and simulation of: heavy-loaded and overloaded systems, complex systems with a large number of possible system states as well as systems engaged for some finite time. These are exactly the systems and working conditions where other methods usually fail.