Silesian University of Technology, Poland

Biography: Tadeusz Czachorski received M.Sc., Ph.D., D.Sc. degrees in informatics respectively in 1972, 1979, 1988, and professor title in 1999. Currently he is a professor at the Silesian University of Technology (Division of Computer Systems Theory and Design) and the director of the Institute of Theoretical and Applied Informatics of Polish Academy of Sciences, IITiS PAN, Gliwice. He spent more than five years at several French universities and research institutes (IRISA Rennes, University of Versailles, ISEM Orsay Paris-Sud, Paris-Nord, National Institute of Telecommunication) and still maintains scientific cooperation with these centres. He participated in Next Generation Internet European project concerning such issues as multiservice-multimedia, mobility, services convergence, quality of service and variable connectivity, where he was co-responsible for the work package concerning analytical, numerical and simulation methods to model performance of the Internet. He took part in Future Internet Engineering project and currently his institute coordinates a European project H2020 on safe and secure Internet of Things. He is a member of programme committees of some periodic international and national conferences, e.g. Heterogeneous Networks HET-NETS, European Workshop on Performance Engineering EPEW, Polish Teletraffic Symposium, Computer Networks, Internet in the Information Society. In 1990 - 2007 he was scientific secretary of the Committee of Informatics of Polish Academy of Sciences, 2007 - 2011 vice-president of this committee, currently member of presidium and head of the section of computer networks and distributed systems of the committee. Chair of IFIP Technical Committee TC5 "Information Technology and Applications" and member of IFIP General Assembly. His scientific interests include mathematical methods and software related to modelling and performance evaluation of wide area computer networks, especially the Internet. The methods include Markov chains, diffusion approximation and fluid flow approximation. They are used to study quality of service, traffic control mechanisms and related problems.

Speech Title: Diffusion Approximation as a tool in computer networks performance evaluation

Abstract: Performance of computer networks is frequently investigated with the use of queueing theory. Its models represent the queues of packets waiting in routers to be sent further and evaluate queueing delays, loss probabilities in routers and then the overall transmission quality of service. There is a constant effort to develop models reflecting as exactly as possible the stochastic nature of the transmission intensity, its variability, the distribution of the size of packets, and the rules of traffic management applied by protocols to avoid network congestion. The article describes one of the approaches: diffusion approximation where the size of queues is described by a diffusion process. The method was introduced in 1970-ties by Hisashi Kobayashi and Erol Gelenbe and is still being developed by the author to fit various models of Internet, Internet of Things, Software Defined Networks, Cloud and Fog computing, edge computing. The method is based on the solution of a system of differential partial equations giving an approximation of the queue lengths distribution at any considered time moment. The features that are in favour of the method are:
- diffusion model of a single server assumes general interarrival and service time distributions this way going beyond Markov models,
- network models may have any topology, also hierarchical, and any number of nodes (are easy scalable)
- the results are obtained in form of queue distributions and waiting time distributions that makes easier to analyse QoS of paths, e.g. jitter,
- easy separation of each node within a network model,
- the transient state model is solved step-by-stem in small time intervals with parameters specific to these intervals; any decision of a controller concerning dynamic routing of packets, as well as changes of flows due to attacks and control mechanisms may be easily reflected in time-dependent and state-dependent diffusion parameters and time-depended routing probabilities in equations determining the flows.