Insurance Call Center 

The following shows the telephone system at an insurance company. Calls come in to the 800 number (black) and are then directed to claims (red) or policy service (blue).

The arrival vector, service rate vector, and routing probabilities for the network are as follows.

In[1]:=

X \[Gamma] = {35, 0, 0}; \[Mu] = {120, 10, 3}; r = {{0, 0.55, 0.45}, {0, 0, 0.02}, {0, 0.01, 0}};

Construct the service channel vector from the diagram.

In[2]:=

X c = {1, 3, 7};

Define the open network for the system.

In[3]:=

X \[ScriptCapitalN] = QueueingNetworkProcess[\[Gamma], r, \[Mu], c];

The total average time spent by a customer in the system is around 17 minutes.

In[4]:=

X (\!\( \*UnderoverscriptBox[\(\[Sum]\), \(i\), \(3\)]\(QueueProperties[{\ \[ScriptCapitalN], i}, "\<MeanSystemSize\>"]\)\))/35

Out[4]=

In[5]:=

X (\!\( \*UnderoverscriptBox[\(\[Sum]\), \(i\), \(3\)]\(QueueProperties[{\ \[ScriptCapitalN], i}, "\<MeanSystemSize\>"]\)\))/35; % 60

Out[5]=