– Random flows of incoming requests, calls, clients and a random manner of servicing them – superimposition of these two randomness factors makes generates enormous difficulties in the analysis of the resultant processes. The size of the queue, the waiting time, and all the related characteristics. Such models are typical not only for structured systems, but also for a wide range of social dynamic problems," said Evsey Morozov, describing the models.
The main area where the theory is applied is computing systems, the Internet, and telecommunication networks. It is also used in logistics, transportation, social systems, in fact, anywhere where there are incoming flows of "requests" arranged randomly and which are handled in a random manner.
Presiding – KarRC RAS Director General Olga Bakhmet and KarRC RAS Secretary for Science Natalya Fokina; speaker – Chief Researcher at IAMR KarRC RAS Evsey Morozov
In his talk, the scientist raised the issues of studying the stability of retrial queuing systems through the regenerative method. Such service models are primarily used to describe the operation of modern wireless telecommunications systems. Their robust operation is a key factor in today's digital environment.
"An important advantage of the regenerative method is its generality and the intuitiveness of the conditions it produces. Such proofs are not only much simpler than those known previously, but are also easily transferable to more general systems, such as systems with outgoing calls," the scientist explained.
Question to the speaker is asked by Yury Zaika, KarRC RAS Deputy Director General, Doctor of Physics and Mathematics
Every year, international conferences are held focusing on the studies of queuing models. Nowadays, this is one of the most topical areas in mathematical science. At the Institute of Applied Mathematical Research KarRC RAS it is addressed by a group of scientists led by Doctor of Physics and Mathematics Evsey Morozov. In September, Alexander Rumyantsev, Senior Researcher at IAMR KarRC RAS, defended his doctoral thesis in this field. Scientists collaborate with leading Russian universities, including Lomonosov Moscow State University, Russian Peoples' Friendship University (RUDN), Tomsk State University, as well as with colleagues from other countries. Last year, the book "Stability Analysis of Regenerative Queueing Models. Mathematical Methods and Applications" by Evsey Morozov, Bart Steyaert was published in Belgium. The researchers annually publish academic articles in reputable international journals.
According to IAMR KarRC RAS Director Vladimir Mazalov, the group will soon be transformed into a designated laboratory.
– The research area that Evsey Viktorovich told us about is a central one for our institute. The research is done at the global level. The queuing theory itself is fascinating, and the research is extremely important: what is happening on the Internet now, all the information and telecommunication processes that are random in nature need to be studied. This is necessary for the network itself," Vladimir Mazalov said.
Director of the Institute of Applied Mathematical Research KarRC RAS Vladimir Mazalov
He also drew an analogy to transport.
– Before we build something, we need to explore the stationarity of these processes. For example, we build city districts and just one road, which will be congested all the time and the queue will be endless. To know this in advance, we need to simulate the situation, study the intensity of the flows, which will be proportional to the number of residents in the area. The speed of service itself will be determined by the width of the road, the number of lanes, traffic lights and so on. It's important. That is why advice from specialists is essential.
Having listened to Evsey Morozov's presentation, members of KarRC RAS Learned Council approved the studies on the stability of the stochastic models of retrial queuing systems conducted at the Institute of Applied Mathematical Research KarRC RAS and recommended that the author uses the results in the personnel training at KarRC RAS postdoctoral school.