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Central Server Network

    
Ten requests circulate in a central server network with three nodes. Balance the load in the network by adjusting the service rate at node 1, which is the central server:
Wolfram Language code: centralserver = QueueingNetworkProcess[(⁠| | | - | | 0 | | 0 | | 0 |⁠), (⁠| | | | | - | --- | --- | | 0 | 0.3 | 0.7 | | 1 | 0 | 0 | | 1 | 0 | 0 |⁠), (⁠| | | ---- | | μ | | 0.5 | | 1.25 |⁠), (⁠| | | - | | 1 | | 1 | | 1 |⁠), 10];
If , the load is concentrated at the central server:
Wolfram Language code: data = RandomFunction[centralserver /. {μ -> 1}, {0, 50}]; ListLinePlot[data, PlotLegends -> Range[3], InterpolationOrder -> 0, Filling -> Axis, PlotRange -> {0, 10}]
By increasing to 2, the balance of the load shifts to the remaining servers:
Wolfram Language code: data = RandomFunction[centralserver /. {μ -> 2}, {0, 50}]; ListLinePlot[data, PlotLegends -> Range[3], InterpolationOrder -> 0, Filling -> Axis, PlotRange -> {0, 10}]