map: Markovian Arrival Process (MAP)

Description Usage Arguments Details Value Note See Also Examples

View source: R/model_map.R

Description

Functions to generate an object of map.

Usage

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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).

See Also

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

Examples

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## 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.