# map: Markovian Arrival Process (MAP) In mapfit: A Tool for PH/MAP Parameter Estimation

## Description

Functions to generate an object of `map`.

## Usage

 ```1 2 3``` ```map(size, alpha, D0, D1, class = "CsparseMatrix") mmpp(size, class = "CsparseMatrix") gmmpp(size, alpha, D0, D1, class = "dgeMatrix") ```

## Arguments

 `size` an integer for the number of phases. `alpha` a vector of probabilities for determing an initial phase. `D0` an object of Matrix class for the initesmal generator without arrivals. `D1` an object of Matrix class for the initesmal generator with arrivals. `class` name of Matrix class for `D0` and `D1`.

## Details

MAP parameters are alpha, D_0 and D_1. alpha is the probability vector to determine an initial phase at time 0. D_0 is an infinitesimal generator of underlyinc continuous-time Markov chain (CTMC) without arrival. D_1 is an infinitesimal generator of CTMC with arrival. The infinitesimal generator of underlying CTMC becomes D_0+D_1. In the stationary case, α is often given by a stationary vector satisfying α (D_0+D_1) = α.

`mmpp` generates an object of a specific MAP called MMPP. MMPP (Markov modulated Poisson process) is an MAP whose D_1 is given by a diagonal matrix. Unlike to general MAPs, MMPP never changes the phase at which an arrival occurs.

`gmmpp` generates an object of `gmmpp`, which is exactly same as MMPP. In the estimation algorithm, `gmmpp` class uses an approximate method.

## Value

`map` gives an object of general MAP. `mmpp` gives an object of MMPP with default parameters. `gmmpp` gives an object of MMPP which uses an approximate estimation algorithm.

## Note

`map` and `gmmpp` require either `size` or (`alpha`, `D0`, `D1`).

`erhmm`, `map.mmoment`, `map.jmoment`, `map.acf`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```## create an MAP (full matrix) with 5 phases map(5) ## create an MAP (full matrix) with 5 phases map(size=5) ## create an MMPP with 5 states mmpp(5) ## create an MMPP with 5 states for approximate ## estimation gmmpp(5) ## create an MAP with specific parameters (param <- map(alpha=c(1,0,0), D0=rbind(c(-4,2,0),c(2,-5,1),c(1,0,-4)), D1=rbind(c(1,1,0),c(1,0,1),c(2,0,1)))) ## marginal moments of MAP map.mmoment(k=3, map=param) ## joint moments of MAP map.jmoment(lag=1, map=param) ## k-lag correlation map.acf(map=param) ```

mapfit documentation built on May 29, 2017, 3:44 p.m.