Package jline.api.pfqn.nc

Class Pfqn_lekt

java.lang.Object
jline.api.pfqn.nc.Pfqn_lekt
public final class Pfqn_lekt extends Object

  • Method Summary

    Modifier and Type
    Method
    Description
    static Ret.pfqnNc
    pfqn_lekt(Matrix L, Matrix N)
     
    static Ret.pfqnNc
    pfqn_lekt(Matrix L, Matrix N, Matrix Z)
    The corrected logistic expansion (pfqn_ble) and the corrected Knessl-Tier expansion (pfqn_bkt) are ONE estimator, evaluated in M-1 and in R dimensions: with a think time their stationary points are one point in dual coordinates (xi_r = N_r/(Z_r + v u'L_r), the class throughputs of the LE fixed point, and v u_k = 1/(1-U_k), the M/M/1 factor of the KT saddle) and Sylvester's identity exchanges the R x R Hessian determinant for the M x M one, after which every 2 pi cancels.
    static String
    route(Matrix L, Matrix N, Matrix Z)
    The side the estimator is computed on: "kt" when R <= M or a class self-loops (one nonzero demand and no think time, which pfqn_kt extracts exactly), "le" otherwise.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • route

      public static String route(Matrix L, Matrix N, Matrix Z)
      The side the estimator is computed on: "kt" when R <= M or a class self-loops (one nonzero demand and no think time, which pfqn_kt extracts exactly), "le" otherwise. The KT side is an R-dimensional convex solve and an R x R determinant, the LE side an M-dimensional fixed point and an (M-1) x (M-1) one.

    • pfqn_lekt

      public static Ret.pfqnNc pfqn_lekt(Matrix L, Matrix N, Matrix Z)
      The corrected logistic expansion (pfqn_ble) and the corrected Knessl-Tier expansion (pfqn_bkt) are ONE estimator, evaluated in M-1 and in R dimensions: with a think time their stationary points are one point in dual coordinates (xi_r = N_r/(Z_r + v u'L_r), the class throughputs of the LE fixed point, and v u_k = 1/(1-U_k), the M/M/1 factor of the KT saddle) and Sylvester's identity exchanges the R x R Hessian determinant for the M x M one, after which every 2 pi cancels. They agree to the accuracy of the two saddle-point solvers. Without a think time the LE branch integrates the radius exactly as Gamma(N+M) while KT Laplaces it, so the two differ by the constant (1-log(2 pi)/2) - r(N+M); the common estimator is defined as the KT value, and the LE side here carries M(1-log(2 pi)/2) - r(N+M) rather than pfqn_ble's (M-1)(1-log(2 pi)/2). See _kb/03-api-layer.md.

    • pfqn_lekt

      public static Ret.pfqnNc pfqn_lekt(Matrix L, Matrix N)