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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:
Wolfram Language code: γ = {35, 0, 0};μ = {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:
Wolfram Language code: c = {1, 3, 7};
Define the open network for the system:
Wolfram Language code: 𝒩 = QueueingNetworkProcess[γ, r, μ, c];
The total average time spent by a customer in the system is around 17 minutes:
Wolfram Language code: (Underoverscript[∑, i, 3]QueueProperties[{𝒩, i}, "MeanSystemSize"]) / 35
Wolfram Language code: % 60