Simulate Message Communication 

Messages arrive at a communication line according to a two-phase hyperexponential distribution with phase probabilities 0.4 and 0.6. The average arrival times for the two phases are 4.8 milliseconds and 0.8 milliseconds, respectively. Simulate the process for 100 milliseconds.

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X communicationLine = RenewalProcess[ HyperexponentialDistribution[{0.4, 0.6}, {1/4.8, 1/0.8}]];

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X ListLinePlot[RandomFunction[communicationLine, {0, 100}, 3], Filling -> Axis, InterpolationOrder -> 0, ImageSize -> 300]

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Shown is the mean number of arrivals during the first 100 milliseconds.

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X Mean[communicationLine[100]]

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Compare with the value obtained from simulation of the time slice distribution.

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X Mean[RandomVariate[communicationLine[100], 10^2]] // N

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