Diffusion approximation as a tool in computer networks performance evaluation, invited talk, The 9th International Conference on Electronics, Communications and Networks, CECNet 2019, October 18-21, 2019 Kitakyushu City, Japan [1]

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.