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MG1StationaryProbability (version 0.1.2)

Computes Stationary Distribution for M/G/1 Queuing System

Description

The idea of a computational algorithm described in the article by Andronov M. et al. (2022) . 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.

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install.packages('MG1StationaryProbability')

Monthly Downloads

205

Version

0.1.2

License

MIT + file LICENSE

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Maintainer

Olga Zoldaka

Last Published

June 13th, 2023

Functions in MG1StationaryProbability (0.1.2)

p0

The stationary probabilities of the environment state 0
EN

Expectation of number of arriving claims depending on i and j
probabilitiesMatrix

Probability matrix calculation. Rows represent arriving probabilities at state i and columns represent the same for state j
pi

Stationary probabilities for continuous time environment's state
ENU

Expectation of number of arriving claims
densityOfSojournTimeAtState_i

The density of the sojourn time in state i with probability that
stationaryProbabilities_cached

Stationary probability caching function
flowIntensityMean

The mean intensity of the arrived flow
h

Density of empty time for initial state i jointly with probability of final state j
finalStateProbability

Probability of the final state
meanTimeOfEmptyPeriod

Mean time of empty period given the stationary probability
not_i

Helper "not i" function
loadCoefficient

Load coefficient
PrTr

Probability to have state j in the ending of the idle period, if initially we have state i
meanSojournTimeWithFSP

Mean sojourn time in the initial state i jointly with final probability of state j
resultingMatrix

Resulting probabilities matrix calculation
serviceDistribution

Service distribution function
meanTimeOfBusyPeriodEW

Mean time of busy period multiplied by load coefficient
b

Service continuous density distribution
probabilityOfNArrival

Probability of n arrival during time t jointly with final state j if initial state is i
meanTimeEmptyFixed

Mean time of empty period in fixed state i
meanSoujournTime

Mean sojourn time in the initial state i (without final probability of state j)
probabilityOfNArrivalW

Probability of n arrival during time t (without joint probability of j)
stationaryProbabilities

Stationary probability function
stationaryProbabilitiesOfEmptyStates

Stationary probabilities of the empty states in continuous time model
MET

Mean idle time if initial state i
MST

Mean empty time sojourn time in the initial state i during the empty period
meanTimeOfBusyPeriodETW

Mean time of busy period
p1

The stationary probabilities of the environment state 1