Package: MG1StationaryProbability 0.1.2

Olga Zoldaka

MG1StationaryProbability: Computes Stationary Distribution for M/G/1 Queuing System

The idea of a computational algorithm described in the article by Andronov M. et al. (2022) <https://link.springer.com/chapter/10.1007/978-3-030-92507-9_13>. The purpose of this package is to automate computations for a Markov-Modulated M/G/1 queuing system with alternating Poisson flow of arrivals. It offers a set of functions to calculate various mean indices of the system, including mean flow intensity, mean service busy and idle times, and the system's stationary probability.

Authors:Olga Zoldaka [aut, cre]

MG1StationaryProbability_0.1.2.tar.gz
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MG1StationaryProbability.pdf |MG1StationaryProbability.html✨
MG1StationaryProbability/json (API)

# Install 'MG1StationaryProbability' in R:
install.packages('MG1StationaryProbability', repos = c('https://mashroommole.r-universe.dev', 'https://cloud.r-project.org'))

Peer review:

Bug tracker:https://github.com/mashroommole/mg1stationaryprobability/issues

On CRAN:

2.00 score 1 scripts 147 downloads 28 exports 8 dependencies

Last updated 1 years agofrom:a0832ee140. Checks:OK: 7. Indexed: yes.

TargetResultDate
Doc / VignettesOKNov 03 2024
R-4.5-winOKNov 03 2024
R-4.5-linuxOKNov 03 2024
R-4.4-winOKNov 03 2024
R-4.4-macOKNov 03 2024
R-4.3-winOKNov 03 2024
R-4.3-macOKNov 03 2024

Exports:bdensityOfSojournTimeAtState_iENENUfinalStateProbabilityflowIntensityMeanhloadCoefficientmeanSojournTimeWithFSPmeanSoujournTimemeanTimeEmptyFixedmeanTimeOfBusyPeriodETWmeanTimeOfBusyPeriodEWmeanTimeOfEmptyPeriodMETMSTnot_ip0p1piprobabilitiesMatrixprobabilityOfNArrivalprobabilityOfNArrivalWPrTrresultingMatrixserviceDistributionstationaryProbabilitiesstationaryProbabilitiesOfEmptyStates

Dependencies:cachemcodetoolsdoParallelfastmapforeachiteratorsmemoiserlang

Readme and manuals

Help Manual

Help pageTopics
Service continuous density distributionb
The density of the sojourn time in state i with probability thatdensityOfSojournTimeAtState_i
Expectation of number of arriving claims depending on i and jEN
Expectation of number of arriving claimsENU
Probability of the final statefinalStateProbability
The mean intensity of the arrived flowflowIntensityMean
Density of empty time for initial state i jointly with probability of final state jh
Load coefficientloadCoefficient
Mean sojourn time in the initial state i jointly with final probability of state jmeanSojournTimeWithFSP
Mean sojourn time in the initial state i (without final probability of state j)meanSoujournTime
Mean time of empty period in fixed state imeanTimeEmptyFixed
Mean time of busy periodmeanTimeOfBusyPeriodETW
Mean time of busy period multiplied by load coefficientmeanTimeOfBusyPeriodEW
Mean time of empty period given the stationary probabilitymeanTimeOfEmptyPeriod
Mean idle time if initial state iMET
Mean empty time sojourn time in the initial state i during the empty periodMST
Helper "not i" functionnot_i
The stationary probabilities of the environment state 0p0
The stationary probabilities of the environment state 1p1
Stationary probabilities for continuous time environment's statepi
Probability matrix calculation. Rows represent arriving probabilities at state i and columns represent the same for state jprobabilitiesMatrix
Probability of n arrival during time t jointly with final state j if initial state is iprobabilityOfNArrival
Probability of n arrival during time t (without joint probability of j)probabilityOfNArrivalW
Probability to have state j in the ending of the idle period, if initially we have state iPrTr
Resulting probabilities matrix calculationresultingMatrix
Service distribution functionserviceDistribution
Stationary probability functionstationaryProbabilities
Stationary probability caching functionstationaryProbabilities_cached
Stationary probabilities of the empty states in continuous time modelstationaryProbabilitiesOfEmptyStates