Investigation at the Extremum on the Average Time Delay of Packages of Self-Similar Traffic Described by the Weibull Distribution
Keywords:Self-similar traffic, Queuing system, QoS characteristics, Weibull distribution, Packet delay time
Background. The development of post-NGN networks leads to an increase in the range of high-speed services that require significant bandwidth and are sufficiently critical to time delays. This determines significant changes in the traffic structure and requires solving the problem of assessing the QoS characteristics when servicing traffic in the post-NGN network. It is possible to find the necessary amount of network resources to support them with the maximum and balanced load of network resources.
Objective. The aim of the paper is to investigate the extremum of some QoS characteristics of self-similar traffic, which is described by means of Weibull distribution.
Methods. Estimation of the average packet delay time of self-similar traffic for the queuing system QS using the Weibull two-parameter distribution and the search for maximum and minimum of the average packet delay time were performed for different conditions of the queuing system operation and different values of packet service intensities and the Hurst parameter.
Results. Value for the average delay time of W packets in QS for different values of service rate packet was defined, and dependence of the average waiting time of W packets in QS from the parameter a, which determines the shape of the Weibull distribution curve, was obtained. It is found that with increasing Hurst parameter, the average delay time value W of packets increases. It means that the increase of the high-speed services (Video Surviliance, smart-TV, HD-video) requires an increase in the size of the buffer devices to provide the required performance of network nodes of post-NGN network.Conclusions. The obtained results allow designing post-NGN network objects taking into account the peculiarities of the construction and structure of the network nodes in the conditions of the real processes of their operation, and provide the ability to set the boundaries of network characteristics, which will provide the necessary QoS. Also, the results of the study will allow the maintenance of self-similar traffic in the post-NGN network of a given structure to provide the necessary performance of network nodes and, accordingly, the size of the buffer devices.
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