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Self-similar traffic in G/M/1 queue defined by the Weibull distribution

Irina V. Strelkovskaya, Tatyna I. Grygoryeva, Irina N. Solovskaya


The work considers a queuing system of the G/M/1 type that simulates service of self-similar traffic in a NodeB (e-NodeB) base station of a mobile operator. The feature of quality of service (QoS) characteristics estimation process for the self-similar traffic defined by the Weibull distribution is the solution based on the Laplace–Stieltjes transformation. The Laplace transformation for an infinite number of items under the Weibull distribution condition was found. It was shown that this series was equiconvergent to some convergence domain. The following QoS characteristics were obtained for the self-similar traffic: the average amount of time that a request spends in the system; the average number of requests waiting in the queue and the average queue length. The obtained results allowed to consider the real values of traffic serviced by a NodeB (e-NodeB) for their optimal deployment over a covered territory at the stage of frequency planning and operation of the 3G/UMTS and 4G/LTE networks.


self-similar traffic; queuing system; QoS characteristics; Weibull distribution; Laplace-Stieltjes transformation; average amount of time that a request spends in the system; average number of requests waiting in the queue; average queue length

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