Package jline.lib.smc

Class MG1_pi

java.lang.Object

jline.lib.smc.MG1_pi

public final class MG1_pi
extends Object

Method Summary

Modifier and Type	Method	Description
static Matrix	mg1_cr(Matrix A)	Computes the G matrix using Cyclic Reduction for M/G/1-type Markov Chains.
static Matrix	mg1_cr(Matrix A, MG1CROptions options)
static Matrix	mg1_pi(Matrix B, Matrix A)
static Matrix	mg1_pi(Matrix B, Matrix A, MG1PiOptions options)	Stationary vector of an M/G/1-type chain by the stable Ramaswami formula.

Methods inherited from class java.lang.Object

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

Method Details

mg1_pi

public static Matrix mg1_pi(Matrix B,
 Matrix A)

mg1_pi

public static Matrix mg1_pi(Matrix B,
 Matrix A,
 MG1PiOptions options)

Stationary vector of an M/G/1-type chain by the stable Ramaswami formula.

A = [A_0 A_1 ... A_dega] repeats from level one, B = [B_0 B_1 ... B_degb] is the boundary row, and G is computed here from the solver named in the options. The recursion is level-by-level, so it costs O(levels * m^3) and not O((levels*m)^3), and it is exact for the chain rather than for a skip-free-to-the-right approximation of it: pi_i = pi_0 R^i holds only in the G/M/1-type case, where a level rises by at most one.

MATLAB twin: MG1_pi.m (SMCSolver, Van Houdt).

mg1_cr

public static Matrix mg1_cr(Matrix A)

Computes the G matrix using Cyclic Reduction for M/G/1-type Markov Chains.

mg1_cr

public static Matrix mg1_cr(Matrix A,
 MG1CROptions options)