Package jline.api.pfqn.sens

Class Pfqn_sens_momldmx

java.lang.Object
jline.api.pfqn.sens.Pfqn_sens_momldmx
public final class Pfqn_sens_momldmx extends Object

  • Method Details

    • pfqn_sens_momldmx

      public static Ret.pfqnSensMom pfqn_sens_momldmx(Matrix lambda, Matrix D, Matrix N, Matrix Z, Matrix mu, Matrix S, Matrix groups)
      Exact moments E[Q], E[Q^2], E[Q^3], variances, skewness and covariances of the queue lengths of a mixed open/closed product-form network with limited load-dependent service rates. This is the load-dependent and mixed counterpart of Pfqn_sens_mom and the higher-order counterpart of Pfqn_sens_mvaldmx.

      By Theorem 1 of Akyildiz and Strelen, with m = E[Q_(j,T)] and y_j scaling the demands of the classes in T at station j: Var = dm/dy_j, E[Q^3] = d^2m/dy_j^2 + (1+3m) dm/dy_j + m^3, and Cov[Q_iT,Q_jT'] = dm_iT/dy_(j,T'). The derivatives come from second-order forward-mode differentiation of the Bruell-Balbo-Afshari mixed load-dependent MVA, i.e. the recursion of pfqn_mvaldmx.

      Reference: I. F. Akyildiz and J. C. Strelen, "Moment Analysis for Load-Dependent Mixed Product Form Queueing Networks", IEEE Trans. Communications 39(6):828-832, 1991, Theorem 1 and eq. (12)-(33).

      Parameters:
      lambda - arrival rate vector (1 x R); zero on closed classes
      D - service demand matrix (M x R)
      N - population vector (1 x R); Inf denotes an open class
      Z - think time vector (1 x R)
      mu - load-dependent rates (M x max(1,sum(N closed))), null for ones
      S - servers per station, accepted for signature compatibility; unused
      groups - class-to-group map (1 x R) with labels 1..G, null for ones(1,R)
      Returns:
      the same struct as Pfqn_sens_mom

    • pfqn_sens_momldmx

      public static Ret.pfqnSensMom pfqn_sens_momldmx(Matrix lambda, Matrix D, Matrix N, Matrix Z, Matrix mu, Matrix S)