# Analyze the Performance of a Queueing Network

#### Define an open queueing network.

 In[1]:= X\[Gamma] = {3, 6}; \[Mu] = {7, 17}; r = {{1/6, 1/9}, {1/4, 1/8}}; c = {1, 1};
 In[2]:= X\[ScriptCapitalN] = QueueingNetworkProcess[\[Gamma], r, \[Mu], c];

#### Simulate the network.

 In[3]:= Xdata = RandomFunction[\[ScriptCapitalN], {0, 10}];

#### Plot the simulated values at the nodes in the network.

 In[4]:= XListLinePlot[data, Filling -> Axis]
 Out[4]=

#### Performance measures at the nodes in the network.

 In[5]:= XTable[QueueProperties[{\[ScriptCapitalN], i}], {i, 2}] // N
 Out[5]=

#### Stationary distribution for the network.

 In[6]:= X\[ScriptCapitalD] = StationaryDistribution[\[ScriptCapitalN]];

#### Probability density function for the steady state of the network.

 In[7]:= XPDF[\[ScriptCapitalD], {m, n}]
 Out[7]=
 In[8]:= XDiscretePlot3D[ PDF[\[ScriptCapitalD], {m, n}] // Evaluate, {m, 0, 4}, {n, 0, 4}, ExtentSize -> 0.5, PlotRange -> All]
 Out[8]=

#### Cumulative distribution function for the steady state of the network.

 In[9]:= XCDF[\[ScriptCapitalD], {m, n}]
 Out[9]=
 In[10]:= XDiscretePlot3D[ CDF[\[ScriptCapitalD], {m, n}] // Evaluate, {m, 0, 35}, {n, 0, 35}, ExtentSize -> Right, PlotRange -> {0, 1.05}]
 Out[10]=