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# fnss.traffic.trafficmatrices.stationary_traffic_matrix

`stationary_traffic_matrix`(topology, mean, stddev, gamma, log_psi, n, max_u=0.9, origin_nodes=None, destination_nodes=None)

  Return a stationary sequence of traffic matrices.

  The sequence is generated by first generating a single matrix assigning traffic volumes drawn from a lognormal distribution and assigned to specific origin-destination pairs using the Ranking Metrics Heuristic method proposed by Nucci et al. [R29]. Then, all matrices of the sequence are generated by adding zero-mean normal fluctuation in the traffic volumes. This process was originally proposed by [R29]

  Stationary sequences of traffic matrices are generally suitable for modeling network traffic over short periods (up to 1.5 hours). Over longer periods, real traffic exhibits diurnal patterns and they are better modelled by cyclostationary sequences

  Parameters: | topology : topology The topology for which the traffic matrix is calculated. This topology can either be directed or undirected. If it is undirected, this function assumes that all links are full-duplex. mean : float The mean volume of traffic among all origin-destination pairs stddev : float The standard deviation of volumes among all origin-destination pairs. gamma : float Parameter expressing relation between mean and standard deviation of traffic volumes of a specific flow over the time log_psi : float Parameter expressing relation between mean and standard deviation of traffic volumes of a specific flow over the time n : int Number of matrices in the sequence max_u : float, optional Represent the max link utilization. If specified, traffic volumes are scaled so that the most utilized link of the network has an utilization equal to max_u. If None, volumes are not scaled, but in this case links may end up with an utilization factor greater than 1.0 origin_nodes : list, optional A list of all nodes which can be traffic sources. If not specified all nodes of the topology are traffic sources destination_nodes : list, optional A list of all nodes which can be traffic destinations. If not specified all nodes of the topology are traffic destinations
  Returns: | tms : TrafficMatrixSequence

  References

  [R29] | (1, 2, 3) Nucci et al., The problem of synthetically generating IP traffic matrices: initial recommendations, ACM SIGCOMM Computer Communication Review, 35(3), 2005

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