Теорія Кернера та фазові переходи для потоків у телекомунікаційних мережах

Abstract

В роботі розглянуто можливість використання теорії Кернера трьох фаз для телекомунікаційних мереж. Описано принципи функціонування транспортних потоків для фаз вільного, синхронізуючого потоків та фази рухомого кластера у системах масового обслуговування з явними втратами, з очікуванням та у системах з повторними викликами. Також розглянуто теорію Кернера за пріоритетного обслуговування та визначено, що кількість фаз значно зростає. Розглянуто можливість дослідження фазових переходів у телекомунікаційних мережах на основі теорії Ландау. Описано параметр порядку, потенціал та коефіцієнт при квадратному члені для дослідження фазових переходів у мережах.

On the basis of experimental three-phase traffic theory for the road considered the possibility of use in telecommunication networks. This theory allows us to describe the car’s transport flows, for the phases of free, synchronized flow and the phase of the moving jams. Three-phase traffic theory for telecommunication networks is described using queueing theory. We consider queueing theory with losses, waiting and recurring calls. The main features and properties of each phase are demonstrated. So, in system with recurring calls serviced all load without recurring calls for phase F. For phase S, all load is fully serviced, but part is serviced a second time, but in the J phase, the load is lost. A comparative analysis has been conducted with the results obtained earlier when investigating the traffic load in an optical transport network. In phase F the transmission time between nodes of the same distance is the same, and without loss. The phases J and S can be distinguished by the existence or non-existence of losses. With a homogeneous network load, the phases can be different for data transfer between nodes and depend on the number of transit nodes between them. At priority service the number of phases increases were shown. The dependence of the number of phases on priorities has been determined. It is impossible that low priority load in the phase with the best properties was taken into account. It was proposed to use new notations that characterize the phases of various priority flows. On the basis of Landau theory the possibility of conducting research on phase transitions in telecommunication networks is considered. For conducting such researches for telecommunication networks have been determined the characteristic of the order parameter. The order parameter can be characterized as the relative losses, waiting and recurring calls. The potential for different number of order parameters is presented. The coefficient for a square member for the study of phase transitions in networks is described. The results for the order parameter for the second-order phase transitions are presented. It was emphasized, using multicomponent order parameters as in physics, the possible existence of additional phases.