Scientists at Tomsk State University (Russia) have created a universal mathematical approach to queuing theory. It allows calculating the most efficient operation of the systems in which the processing of incoming flow takes place. In particular, it can be used to eliminate queues in shops and banks and eliminate mobile communication congestion during the holidays.
"We are all faced with situations in the New Year or other holidays when we cannot get on the telephone because the system is overloaded. Mathematical calculations, particularly the methods of queuing theory, allow solving such problems," says Svetlana Moiseeva, professor at Tomsk State University (TSU). Creating and studying the mathematical models of real telecommunication streams, information systems, and computer networks is very relevant today.
The team, led by Professor Anatoly Nazarov, has for several years been developing mathematical models and methods to solve a very broad class of problems associated with queuing. "We have derived the general formula for the calculation. It is enough to substitute for the variables specific parameters, such as the number of servers, towers, communication channels, and others, and determine under what conditions the system will run smoothly," says Nazarov. "Using this method will enable significant savings on upgrades, for example, reducing the risk of buying equipment that will stand idle."
Scientists say this method is so universal that it is suitable for calculating the efficiency of multiple service systems—in retail, insurance companies, banks, ports, and other industries. In addition, the technique could predict the functioning of such systems to make effective management decisions.
The research results were published in the European Journal of Operational Research. The report was read at the International Symposium on Systems with Repeated Calls, held in Amsterdam. It made such an impression that the symposium organizing committee proposed to hold the next meeting in 2018 at Tomsk State University.
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Alexander Moiseev et al, Queueing network MAP−K(GI/∞) with high-rate arrivalsEuropean Journal of Operational Research (2016). DOI: 10.1016/j.ejor.2016.04.011