MG1_piKt

All Implemented Interfaces:


public final class MG1_piKt

Nested Class Summary

Nested Classes
Modifier and Type	Class	Description

Field Summary

Fields
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Constructor Summary

Constructors
Constructor	Description

Enum Constant Summary

Enum Constants
Enum Constant	Description

Method Summary

Modifier and Type	Method	Description
`final static Matrix`	`mg1_pi(Matrix B, Matrix A, MG1PiOptions options)`	Computes the stationary distribution of an M/G/1-type Markov chain.
`final static Matrix`	`mg1_cr(Matrix A, MG1CROptions options)`	Computes the G matrix using Cyclic Reduction for M/G/1-type Markov Chains.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
- Method Detail
  - mg1_pi
```
 final static Matrix mg1_pi(Matrix B, Matrix A, MG1PiOptions options)
```
    Computes the stationary distribution of an M/G/1-type Markov chain.
    The chain is characterized by:
    B: boundary blocks B0 B1 B2 ... B_maxb with m rows
    A: repeating blocks A0 A1 A2 ... A_maxa with m rows
    Parameters:
    
    B - Boundary block matrix (or null to use first row of A)
    
    A - Repeating block matrix
    
    options - Solver options
    
    Returns:
    
    Stationary distribution vector
  - mg1_cr
```
 final static Matrix mg1_cr(Matrix A, MG1CROptions options)
```
    Computes the G matrix using Cyclic Reduction for M/G/1-type Markov Chains.
    Solves: G = A0 + A1G + A2G^2 + ... + A_max*G^max
    Implements the Point-Wise Cyclic Reduction (PWCR) and Shift+PWCR algorithms from Bini and Meini, using DFT for point-wise evaluation at roots of unity.
    
    Parameters:
    
    A - Block matrix A0 A1 A2 ...
    
    options - Solver options
    
    Returns:
    
    G matrix (minimal nonnegative solution)