| Function name and call pattern for Mathlink functions (1) | Function name for Mathematica functions | Short description of the function |
| Markov Processes | ||
| - | CtMarkovChain[Matrix] (MMA) | Gives the stationary probabilities of a continuous time Markov chain with the transition rate matrix Q. |
| - | DtMarkovChain[Matrix] (MMA) | Gives the stationary probabilities of a discrete time Markov chain with the transition probability matrix P. |
| Loss Systems | ||
| - | MVA[Matrix, Vector, Vector] (MMA) | Algorithm for the Mean Value Analysis of a closed Jackson network. It returns the average queue lengths and the average sojourn times in the queues. The branching ratios are given by the matrix R; the vector mu specifies the service rates of the queues; and K is the number of customers in the network. |
| LnkBerli[Integer, Real] (2) | Berli[Integer, Real] (MMA) | Erlang loss probability. |
| LnkBerld[Real, Real] (2) | Berld[Real, Real] (MMA) | Erlang loss probability. |
| LnkXerl[Real, Real] | Xerl[Real, Real] (MMA) | Inverse Erlang function. |
| LnkAerl[Real, Real] | Aerl[Real, Real] (MMA) | Inverse Erlang function. |
| LnkBkaufman[Integer, Integer, Integer, IntegerList, RealList] | - | Erlang blocking probability for multiple traffic classes. |
| LnkBmitra[Integer, Integer, Real, IntegerList, RealList] | - | Erlang blocking probability for multiple traffic classes. |
| GAMS (3) | - | Anick-Mitra-Sondhi handling function. |
| EvAMS (3) | - | Anick-Mitra-Sondhi handling function. |
| initAMS (3) | - | Anick-Mitra-Sondhi handling function. |
| freeAMS (3) | - | Anick-Mitra-Sondhi handling function. |
| M/D/1 etc Queuing Systems | ||
| LnkQmd1[Real, Real] | Qmd1[Real, Real] (MMA) | Virtual waiting time distribution for the M/D/1 queue. |
| LnkQndd1[Real, Integer, Real] | Qndd1[Real, Integer, Real] (MMA) | Virtual waiting time distribution for the N*D/D/1 queue. |
| LnkQsdd1[Real, RealList] | Qsdd1[Real, RealList] (MMA) | Virtual waiting time distribution for the ∑ Di/D/1 queue. |
| LnkMg1[Integer, Real, Integer] | Mg1[Integer, Real, Function] (MMA) (4) | Queue length probability function for the M/G/1 queue. |
| LnkQmxd[Real, Real, RealList] | Qmxd[Real, Real, RealList] (MMA) | Unfinished work tail distribution function for the Mx/D/1 queue. |
| LnkFmd1[Real, Real] | Fmd1[Real, Real] (MMA) | Virtual waiting time distribution for the M/D/1 queue. |
| LnkIntFmd1[Integer, Real] | IntFmd1[Integer, Real] (MMA) | Virtual waiting time distribution for integral values of the amount of unfinished work in the system. |
| LnkSumMd1[Real, Real] | SumMd1[Real, Real] (MMA) | Calculates state probabilities of the M/D/1 queue. |
| LnkRecMd1[Integer, Real] | RecMd1[Integer, Real] (MMA) | Calculates state probabilities of the queue with a recursive algorithm. |
| LnkFmdn[Real, Real, Integer] | Fmdn[Real, Real, Integer] (MMA) | Virtual waiting time distribution of the M/D/n queue. |
| LnkIntFmdn[Integer, Real, Integer] | IntFmdn[Integer, Real, Integer] (MMA) | Virtual waiting time distribution for integral values of the amount of unfinished work in the system. |
| LnkMdn[Real, Real, Integer] | Mdn[Real, Real, Integer] (MMA) | Calculates state probabilities of the M/D/n queue. |
| LnkFekdn[Real, Real, Integer, Integer] | Fekdn[Real, Real, Integer, Integer] (MMA) | Virtual waiting time distribution for the Ek/D/n queue. |
| LnkFend1[Real, Integer, Real] | Fend1[Real, Integer, Real] | Virtual waiting time distribution for the En/D/n queue. |
| Network generation etc | ||
| LnkGabrielNet[Integer] (5) | GabrielNet[Integer] (5) | Generates a random network based on Gabriel criterion. |
| LnkDijkstra[DistanceMatrix, Integer, Integer] (5) | Dijkstra[DistanceMatrix, Integer, Integer] (5) | Finds out the shortest path from the given root node to the given destination node. |
| - | ShowNetwork[Output_GabrielNet, Output_Dijkstra] (5) | Creates graphs of the network and the route(s). |
| - | NormalizationConstant[List] (MMA) (6) | Calculates the normalization constant for a tree network with balanced fair capacity allocation. Input is a list describing the tree and offered flows. |
| - | Throughputs[List] (MMA) (6) | Calculates the normalization constant and flow throughputs for a tree network with balanced fair capacity allocation. Input is a list describing the tree and offered flows. Output is a list: {normalization constant, {throughputs}, {flows}}. |
| - | TreeGraph[List] (MMA) (6) | Returns a graphics object for drawing a tree network. Input is a list describing the tree and offered flows. |
(1) These are the MathLink function names. The "original" C-functions lack the Lnk- prefix and their call pattern is different. Click on the link of each function for further information.
(2) The C-functions are called Berl_i and Berl_d.
(3) Anick-Mitra-Sondhi handling functions are not included in the qlib -file and cannot be used via MathLink. No Mathematica -versions of these functions are either available.
(4) Here is an example: first we define function F: F[t_] := If[t < 1, 0, 1] in Mathematica, and then we use Mg1: Mg1[3, 0.4, F].
(5) More specific and detailed descriptions can be found in the qlib.m file or after installing the Mathematica-package typing eg. ?Dijkstra in the Mathematica.
(6) See the notebook norm_constant.nb for more details.
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