Package jline.api.npfqn

Class Npfqn_traffic_rqt

java.lang.Object
jline.api.npfqn.Npfqn_traffic_rqt
public final class Npfqn_traffic_rqt extends Object

  • Method Details

    • npfqn_traffic_rqt

      public static double[][] npfqn_traffic_rqt(double[] lambda0, double[] Gamma0, double[] alpha0, Matrix F)
      Effective arrival process perceived at each node of a single-class open queueing network under the Robust Queueing Theory calculus. The characterization composes three operators: passage through a queue with adversarial servers leaves the uncertainty set unchanged (robust Burke, Theorem 4), superposition merges sets by Theorem 5, and thinning by a fraction f scales the rate by f and the variability by f^(-1/alpha) (Theorem 6). The resulting equations are lambda_j = lambda0_j + sum_i lambda_i f_ij and Gamma_j = (1/lambda_j) [ 1{a0_j=ab_j} (lambda0_j Gamma0_j)^(p_j) + sum_i 1{ab_i=ab_j} (lambda_i Gamma_i)^(p_i) f_ij ]^(1/p_j), with p_j = ab_j/(ab_j-1) and ab_j the minimum tail coefficient among the streams feeding j: the heaviest tail upstream dominates.

      Both are solved exactly rather than iteratively. The rate equations are the usual traffic equations, and in the variables z_j = (lambda_j Gamma_j)^(p_j) the variability equations are linear as well, so each is one linear system; ab is obtained by propagating the minimum to a fixed point.

      Parameters:
      lambda0 - external arrival rate at each node, 0 where there is none
      Gamma0 - variability parameter of each external arrival process, which for a renewal stream is the interarrival standard deviation
      alpha0 - tail coefficient in (1,2] of each external arrival process
      F - routing probability matrix, F(i,j) = fraction of the jobs leaving node i that go to node j (row sums <= 1)
      Returns:
      array {lambda, Gamma, alpha} of length-J vectors: the effective arrival rate, variability parameter and tail coefficient at each node