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Oil Change Center Queue

Cars arrive at an oil change center following a Poisson process, at the rate of four per hour. There is a single available mechanic, and the time taken to perform an oil change is exponentially distributed, with an average of 12 minutes. Approximate an unlimited car space.

    
Wolfram Language code: 𝒫 = QueueingProcess[4, 60 / 12];
Steady-state distribution for the system:
Wolfram Language code: 𝒟 = StationaryDistribution[𝒫];
Distribution for the number of cars in the system:
Wolfram Language code: DiscretePlot[PDF[𝒟, k], {k, 1, 20}, ExtentSize -> 0.5, PlotRange -> All]
Probability that there are more than three cars at the oil change center:
Wolfram Language code: NProbability[x > 3, x𝒟]
Mean and variance for the number of cars in the system:
Wolfram Language code: {Mean[𝒟], Variance[𝒟]}//N