Fluctuations, Averages, and Non-linearity

This approach is well known to us from a different part of the engineering knowledge base thermodynamics. For example, the pressure, P, of a volume, V, of gas is the average of the forces exerted by the individual molecules on the boundary of the volume, and the macroscopic behaviour of the gas is described by the simple equation PV = RT. This relationship between the three parameters P, V, and T holds as they change in time as part of some process, but the change must be slow compared to the timescale on which the microscopic collision processes take place, so that at any point in time, these microscopic processes experience essentially a static or equilibrium environment. 

The second example is a system of buses providing a transport service. An important service parameter is the arrival time of buses in relation to the scheduled 

To be able to handle the effect of fluctuations in the service parameters due to non-linear value functions, while at the same time retaining much of the simplicity of the linear case, the following model of the value function can be useful. 

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