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Random Processes
Continuous-Time and Discrete-State Processes
In[1]:=
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procs = {PoissonProcess[1.3], TelegraphProcess[1.3], ContinuousMarkovProcess[{1, 0, 0}, {{0, 1/2, 1/2}, {1/2, 0, 1/2}, {1/2, 1/2, 0}}, {1, 2, 1}], QueueingProcess[1, 2], QueueingNetworkProcess[\!\(\* TagBox[ RowBox[{"(", "", TagBox[GridBox[{ {"0"}, {"0"}, {"0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}], Column], "", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\), \!\(\* TagBox[ RowBox[{"(", "", GridBox[{ {"0", "0.3", "0.7"}, {"1", "0", "0"}, {"1", "0", "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}], "", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\), \!\(\* TagBox[ RowBox[{"(", "", TagBox[GridBox[{ {"1"}, {"0.5"}, {"1.25"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}], Column], "", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\), \!\(\* TagBox[ RowBox[{"(", "", TagBox[GridBox[{ {"1"}, {"1"}, {"1"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}], Column], "", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\), 10], RenewalProcess[GammaDistribution[2, 1]], CompoundPoissonProcess[.8, DiscreteUniformDistribution[{-2, 2}]], CompoundRenewalProcess[GammaDistribution[2, 1.7], DiscreteUniformDistribution[{-2, 2}]]};
In[2]:=
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data = RandomFunction[#, {0, 25}] & /@ procs;
In[3]:=
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plots = Table[ ListLinePlot[data[[i]], PlotLabel -> Head[procs[[i]]], Filling -> Axis, InterpolationOrder -> 0, PlotRange -> All, FillingStyle -> Directive[Opacity[0.5], RandomChoice[ColorData[45, "ColorList"]]]], {i, Length[procs]}]
Continuous-time and discrete-state processes.
Out[3]=
