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

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.

Olga Zoldaka

MG1StationaryProbability

Computes Stationary Distribution for M/G/1 Queuing System

h function

<dl><dt>i</dt>
<dd>MC i-th state</dd>
<dt>j</dt>
<dd>MC j-th state</dd>
<dt>t</dt>
<dd>time value</dd>
<dt>m</dt>
<dd>distribution parameters vector of sojourn times
in alternating environment states</dd>
<dt>lambda</dt>
<dd>Poisson flow intensity vector</dd></dl>

Arguments

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

<dl>

<dt>i</dt>
<dd>MC i-th state</dd>


<dt>j</dt>
<dd>MC j-th state</dd>


<dt>t</dt>
<dd>time value</dd>


<dt>m</dt>
<dd>distribution parameters vector of sojourn times
in alternating environment states</dd>


<dt>lambda</dt>
<dd>Poisson flow intensity vector</dd>

</dl>

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

Description

Usage

Value

Arguments

Examples