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Principle (Variability Propagation): The variability of outputs from a station increases in both the arrival variability and the process variability at the station.

The output process of the first station of the line becomes the input process or the arrival process of the second station in the line. Similarly, the output process of the second station of the line becomes the arrival process of the third station in the line, and so on throughout the line. Hence, if outputs from an upstream station are variable (bursty), then inputs to the downstream station will be variable.

The variability of the output process of a single station is affected by the arrival variability, the process variability and the utilization of the station. The following four scenarios summarize the ways that variability can propagate through a single station.

For example in the first case illustrated below, we have low arrival variability, high process variability, and high utilization. At a station like this, high utilization will cause a large queue to build up.  Hence, interoutput times will essentially be process times at the station and therefore output variability will closely resemble process variability (in terms of the coefficient of variation).

In contrast, consider the second case illustrated below.  Here, station utilization is low.  So a queue rarely builds at the station and therefore the spacing of outputs is governed more by the spacing of arrivals than by process times.  In this case, smooth arrivals lead to smooth departures, even though the process times themselves are variable (i.e., because the process times are short relative to interarrival times in a low utilization station).

The other cases have similar interpretations.
 

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